It does not look promising.
INA 314: INELIGIBILITY TO NATURALIZATION OF DESERTERS FROM THE ARMED FORCES OF THE UNITED STATES
Sec. 314. [8 U.S.C. 1425] A person who, at any time during which the United States has been or shall be at war, deserted or shall desert the military, air, or naval forces of the United States, or who, having been duly enrolled, departed, or shall depart from the jurisdiction of the district in which enrolled, or who, whether or not having been duly enrolled, went or shall go beyond the limits of the United States, with intent to avoid any draft into the military, air, or naval service, lawfully ord ered, shall, upon conviction thereof by a court martial or a court of competent jurisdiction, be permanently ineligible to become a citizen of the United States; and such deserters and evaders shall be forever incapable of holding any office of trust or of profit under the United States, or of exercising any rights of citizens thereof.
SEE:
http://www.state.gov/documents/organization/87030.pdf
A small excerpt:
9 FAM 40.82 N5.3 Aliens Ineligible to Citizenship Not Affected by Pardon
(TL:VISA-46; 08-26-1991)
The Presidential pardon provides no relief for an alien found ineligible under the first part of INA 212(a)(8)(B) as an alien who is ineligible for citizenship i.e., a person who was convicted of either desertion from or leaving the country to evade military service. [See INA 314, 9 FAM 40.82 Related Statutory Provisions.] Ineligibility to citizenship because of seeking and obtaining exemption from service on the grounds of alienage is irrelevant in this context.
Jimmy Carter Pardon:
http://www.justice.gov/pardon/executive_order.htm
9 FAM 40.82 N6 EFFECT OF DISCHARGE ON DESERTERS
(TL:VISA-4; 11-19-1987)
A deserter who subsequently received a discharge may (or may not) have been relieved of such ineligibility, depending on the disposition of the desertion aspect of the case by the appropriate branch of service. Any desertion involving a subsequent discharge must be referred to the Department (CA/VO/L/A) for an advisory opinion.
SEE:
http://www.uscis.gov/ilink/docView/SLB/HTML/SLB/0-0-0-1/0-0-0-45104.html
Interpretation 314.1 Deserters; draft evaders.
Since the Act of March 3, 1865, similar statutory provisions 1/ have prohibited the naturalization of enrolled draft evaders and deserters from the Untied States armed forces. As amended but the Act of August 3, 1912, the Revised Statutes limited ineligibility to war-time desertions, a limitation that has been reflected in all subsequent legislation.
Interpretation 314.2 Effect of pardon and amnesty.
A deserter who is unconditionally pardoned by the President is relieved from penalties imposed by law and thus may apply for naturalization. 7/
Under authority contained in the Act of March 3, 1865, as amended in 1912, 8/ the President by proclamation dated March 5, 1924, 9/ granted an amnesty to all World War I participants who deserted on or after November 11, 1918, the date upon which actual hostilities ceased and prior to July 2, 1921, the date on which the war formally ended.
An amnesty and pardon similar to that above was conferred upon all who deserted during World War II, if the offense was committed on or after August 14, 1945, the date active hostilities terminated, and before June 25, 1950, the date of the Korean invasion. 10/
As to all the above persons, the statutory bar to naturalization contained in former legislation and the current statute was removed by these proclamations.
For desertion or draft evasion as a basis for expatriation under the current law see INTERP 349.
A desertion commenced during a time of peace is not considered a war-time desertion within the above requirement, even if continued after the outbreak of hostilities.
The period of the Korean conflict constiuted a time of war within the meaning of the 1940 legislation. 1/ , 2/
While conviction of desertion by court martial was first required by the above 1940 statute, the courts imposed a similar requisite under the earlier law; 3/ and, neither an admission of desertion, 4/ a finding of desertion by a civil court, 5/ nor a listing of a person on official military records as a deserter 6/ precluded naturalization in the absence of the required conviction.
The existing law provides for conviction by a court of competent jurisdiction as well as by court martial, and extends ineligibility to the draft evader who has not been enrolled under the conscriptive statute.
FROM:
http://www.veteransforamerica.org/wp-content/uploads/2008/11/28-Immigration.pdf
Less-than-Honorable Discharge, Desertion, Failure to Appear for Induction, Draft Avoidance Based on Alienage
Persons not honorably discharged may not avail themselves of the special rules that apply to those in active service. Further, citizenship granted because of service in the U.S. military may be revoked if the person is dishonorably discharged at any point prior to five years of honorable service. However, a dishonorable discharge and the crime of failure to appear for induction do not necessarily indicate a lack of good moral character and do not bar naturalization.
Note that military law describes five types of discharges: honorable discharge, general discharge under honorable conditions, discharge under other than honorable conditions, bad conduct discharge and dishonorable discharge. The USCIS considers an honorable discharge and general discharge under honorable
conditions to meet the definition of “honorable discharge.”
Desertion is a permanent bar to naturalization. However, if you are the beneficiary of an individual pardon or a group pardon for any crime or offense, including desertion, you may naturalize.
Non-citizens who avoided the draft because they are not citizens are not eligible to apply for naturalization, though many exceptions apply.