Is it possible for a person who in in the country illegally to "slip" through and join the US Armed Forces?

It is possible. I know this because we have caught them after the fact. In one case we learned a soldier was not in country legally when he was preparing to ship to Iraq. That was over a year ago so I would hope we have done a better job now checking documents.

Edit: CPIEFLY did not answer the actual question. the question pertained to entering the military as an illegal, not as a non-American. There is a difference. As long as you are in America legally with the proper documents that allow enlistment, you may enter. If you simply slip across the border, you may not. Also, the military does not have special programs which allow you to become a citizen quicker. The military has no programs for allowing anyone to become a citizen. USCIS has the responsibility for this just as DoS is responsible for normal the normal Visa process. DoS and USCIS have programs under which service in the US Military allows you to become a citizen sooner, but that is their program, not ours.

YES! It happens all the time. Being a citizen is not a requirement to serve in the US Armed Forces. It is quite surprising! There are certian positions that require higher security clearances, which cannot be given to non-citizens. The military even has special programs that make it easier to become a citizen, in an attempt to have more "non citizens" to join and help the military recruiting goals.

This is a highly debatable topic within the military.

It is possible, it has happened before.

But , when they are found out, they are discharged from the military.

no.