No, they can't apply for US passport. Only US citizen can apply for a US passport, NOT US born person. I hope you notice the difference. The children born to diplomats are diplomats as well, because they are given the legal status of their parents. Let us not be technical here, they can't hold a diplomatic office, is is the classification I believe is A1 visa. Enforcement is NOT the concern of DoS, because all foreign diplomats are fully aware of their rights and privileges, so there no need to try to claim US citizenship. Also, let us face it, most diplomats are the who and who in their own countries, NOT someone who want to remain permanent with their children in the US. In addition, within the DoS, there are couple of units which are devoted to dealing with people on the diplomatic corps, which include the facilitation of issuance of SSN for diplomats, letters to obtain drivers licenses. Once you have a diplomatic imminuty from US laws, simple things such as obtaining a drivers license are regulated by DoS, and I know this because when I went to obtain my driver's license, the DoS issues numerous letters to DC DMV, and I went to a DMV which served diplomats and people working for UN and World Bank Group organization, not your regular dog-eat-dog DMV. Once you are at DMV, they assign someone to review and verify your credentials, because your visa is a different legal status than a student visa, and review DoS documentation, and issue the DL. Once you complete some of the application forms required for DL, they issue the DL and you are out of the place in a jiffy... Try doing that at a usual DMV with your own preparation without the might of DoS, this is what will happen to you...
http://www.hulu.com/watch/54637/family-guy-dmv
Please read my post ...I did not say apply for US Passport ..said apply for USC (US Citizenship) which are different things...I understand all about diplomatic priveledges and immunity...that is being said, we are talking about children who are born in USA. Children when they are adults can apply for SSN by producing Birthcertificates....but that is not my question....my question was: can they apply for any US immigration benefits up to USC under the current law ?