Do you REALLY have to travel? IF you are deemed to have shown your "immigrant intent" and your case has not progressed to the point where you have filed an I-485 fior adjustment and obtained Advance Parole based on a pending adjustment, you may be refused re-entry as a J-1 non-immigrant who is suppossed to have a foreign residence that (s)he has NO INTENTION OF ABANDONING. Travel outside the U.S. may be a bad idea right now.
J-1 visa is defined in the INA at Section 101(a)(15)--
(J) an alien having a residence in a foreign country which he has no intention of abandoning who is a bona fide student, scholar, trainee, teacher, professor, research assistant, specialist, or leader in a field of specialized knowledge or skill, or other person of similar description, who is coming temporarily to the United States as a participant in a program designated by the Director of the United States Information Agency, for the purpose of teaching, instructing or lecturing, studying, obser ving, conducting research, consulting, demonstrating special skills, or receiving training and who, if he is coming to the United States to participate in a program under which he will receive graduate medical education or training, also meets the requirements of section 212(j), and the alien spouse and minor children of any such alien if accompanying him or following to join him;
Your biggest hurdle to getting a greencard (or switching to an H1-B visa) is the potential subjection to INA 212 (e)---
(e) No person admitted under section 101(a)(15)(J) or acquiring such status after admission (i) whose participation in the program for which he came to the United States was financed in whole or in part, directly or indirectly, by an agency of the Government of the United States or by the government of the country of his nationality or his last residence, (ii) who at the time of admission or acquisition of status under section 101(a)(15)(J) was a national or resident of a country which the Director of the United States Information Agency pursuant to regulations prescribed by him, had designated as clearly requiring the services of persons engaged in the field of specialized knowledge or skill in which the alien was engaged, or (iii) who came to the United States or acquired such status in order to receive graduate medical education or training, shall be eligible to apply for an immigrant visa, or for permanent residence, or for a nonimmigrant visa under section 101(a)(15)(H) or section 101(a)(15)(L) until it is established that such person has resided and been physically present in the country of his nationality or his last residence for an aggregate of a least two years following departure from the United States: Provided, That upon the favorable recommendation of the Director, pursuant to the request of an interested United States Government agency (or, in the case of an alien described in clause (iii), pursuant to the request of a State Department of Public Health, or its equivalent), or of the Com missioner of Immigration and Naturalization after he has determined that departure from the United States would impose exceptional hardship upon the alien's spouse or child (if such spouse or child is a citizen of the United States or a lawfully resident alien), or that the alien cannot return to the country of his nationality or last residence because he would be subject to persecution on account of race, religion, or political opinion, the Attorney General may waive the requirement of such two-year foreig n residence abroad in the case of any alien whose admission to the United States is found by the Attorney General to be in the public interest except that in the case of a waiver requested by a State Department of Public Health, or its equivalent, or in the case of a waiver requested by an interested United States government agency on behalf of an alien described in clause (iii), the waiver shall be subject to the requirements of section 214(l) 22aaa/ : And provided further, That, except in the case of an alien described in clause (iii), the Attorney General may, upon the favorable recommendation of the Director, waive such two-year foreign residence requirement in any case in which the foreign country of the alien's nationality or last residence has furnished the Director a statement in writing that it has no objection to such waiver in the case of such alien.
And then again, you could fall under INA 212(j) provisions:
(j) (1) The additional requirements referred to in section 101(a)(15)(J) for an alien who is coming to the United States under a program under which he will receive graduate medical education or training are as follows:
(A) A school of medicine or of one of the other health professions, which is accredited by a body or bodies approved for the purpose by the Secretary of Education, has agreed in writing to provide the graduate medical education or training under the program for which the alien is coming to the United States or to assume responsibility for arranging for the provision thereof by an appropriate public or nonprofit private institution or agency, except that, in the case of such an agreement by a schoo l of medicine, any one or more of its affiliated hospitals which are to participate in the provision of the graduate medical education or training must join in the agreement.
(B) Before making such agreement, the accredited school has been satisfied that the alien
(i) is a graduate of a school of medicine which is accredited by a body or bodies approved for the purpose by the Secretary of Education (regardless of whether such school of medicine is in the United States); or
(ii)(I) has passed parts I and II of the National Board of Medical Examiners Examination (or an equivalent examination as determined by the Secretary of Health and Human Services),
(II) has competency in oral and written English,
(III) will be able to adapt to the educational and cultural environment in which he will be receiving his education or training, and
(IV) has adequate prior education and training to participate satisfactorily in the program for which he is coming to the United States. For the purposes of this subparagraph, an alien who is a graduate of a medical school shall be considered to have passed parts I and II of the National Board of Medical Examiners examination if the alien was fully and permanently licensed to practice medicine in a State on January 9, 1978, and was practicing medicine in a State on that date.
(C) The alien has made a commitment to return to the country of his nationality or last residence upon completion of the education or training for which he is coming to the United States, and the government of the country of his nationality or last residence has provided a written assurance, satisfactory to the Secretary of Health and Human Services, that there is a need in that country for persons with the skills the alien will acquire in such education or training.
(D) The duration of the alien's participation in the program of graduate medical education or training for which the alien is coming to the United States is limited to the time typically required to complete such program, as determined by the Director of the United States Information Agency at the time of the alien's admission into the United States, based on criteria which are established in coordination with the Secretary of Health and Human Services and which take into consideration the publish ed requirements of the medical specialty board which administers such education or training program; except that-
(i) such duration is further limited to seven years unless the alien has demonstrated to the satisfaction of the Director that the country to which the alien will return at the end of such specialty education or training has an exceptional need for an individual trained in such specialty, and
(ii) the alien may, once and not later than two years after the date the alien is admitted to the United States as an exchange visitor or acquires exchange visitor status, change the alien's designated program of graduate medical education or training if the Director approves the change and if a commitment and written assurance with respect to the alien's new program have been provided in accordance with subparagraph (C).
(E) The alien furnishes the Attorney General each year with an affidavit (in such form as the Attorney General shall prescribe) that attests that the alien (i) is in good standing in the program of graduate medical education or training in which the alien is participating, and (ii) will return to the country of his nationality or last residence upon completion of the education or training for which he came to the United States.
(2) An alien who is a graduate of a medical school and who is coming to the United States to perform services as a member of the medical profession may not be admitted as a nonimmigrant under section 101(a)(15)(H)(i)(b) unless-
(A) the alien is coming pursuant to an invitation from a public or nonprofit private educational or research institution or agency in the United States to teach or conduct research, or both, at or for such institution or agency, or
(B) (i) the alien has passed the Federation licensing examination (administered by the Federation of State Medical Boards of the United States) or an equivalent examination as determined by the Secretary of Health and Human Services, and
(ii)(I) has competency in oral and written English or
(II) is a graduate of a school of medicine which is accredited by a body or bodies approved for the purpose by the Secretary of Education (regardless of whether such school of medicine is in the United States).
(3) The Director of the United States Information Agency annually shall transmit to the Congress a report on aliens who have submitted affidavits described in paragraph (1)(E), and shall include in such report the name and address of each such alien, the medical education or training program in which such alien is participating, and the status of such alien in that program.
