Maybe they do and maybe they don't. It's an interesting article.
Illegals in the Military
March 1, 2004
An article in The Denver Post on Feb. 24 [2004] stated that the U.S. military does not know the citizenship status of 16,031 active-duty military personnel...
In a recent article ("The Illegal Immigration Threat," DefenseWatch, Jan. 14, 2004), I talked about a 19-year old illegal alien who used a bogus green card to enlist in the Army, and how the Army was going to help facilitate getting him citizen status. (The Army's efforts did result in that soldier being sworn in as a U.S. citizen.) The Denver Post article reported:
"[T]he citizenship of 16,031 members of the Army, Air Force, Navy and Marines is listed as 'unknown.' That's about one in 100 active-duty military members who might be U.S. citizens, legal immigrants - or just about anybody else.""U.S. military officials say they are shoring up defenses against illegal immigrants and others who may misrepresent themselves and join the armed services."
"The Army has the highest number of unknowns - 9,055. The Navy has 6,531, the Air Force 444, the Marines one. Overall, 1,366,032 U.S. citizens and 35,662 legal immigrants serve in the U.S. military."
"The case of an Army private from Mexico, who enlisted using a fake green card and then served in Iraq, suggests some of the unknowns could be illegal immigrants. The military has no set procedure for handling these cases. U.S. congressional leaders are looking into the matter ... Some experts see a security risk. Military officials say they've had few problems so far, but the 9/11 terrorist attacks raised concerns."
snip
I know when I was in the Air Force we had some legal immigrants in our squadron. They were all working towards citizenship and many made it. I just presumed a legal status in this country would be required before any background checks could be conducted for classification purposes.