It was when I went through. No citizenship or green card, no play. Unless something has changed since '02. And I'm sure they do at least a cursory background check. At least I'd hope they did after I spent 3 days filling out that SF 86. 
Speaking of hunger strikes, I saw a bunch of signs around campus yesterday talking about "HUNGER!" Not sure if they were related to these idiots since they were written on cardboard boxes in what looked like colored pencil. The ISO was also out there too. Is it me, or can you actually smell those people before you see them?
It's a fake issue, I think, to tart up the amnesty proposal so it looks like it's accomplishing something positive. The only way an illegal is getting in is through identity theft, which would get them thrown out on fraudulent enlistment for the identity theft, NOT for being an illegal, when it was discovered.
eta - I guess on second thought it is possible there might be a very small number of people raised from tots in the US who were brought in illegally, and either their parents faked identities for them or they live in a state that has some way to explain why they didn't get a normal birth cert, like 'correcting' an 'unregistered home birth.' In that kind of case it wouldn't be a fraudulent enlistment, but I can't imagine this is a high-frequency situation.