i guess yes...but that is not the big issue , the big one will be how u get in after getting caught by us border?
here is what i think: if after that u went through a kind of process & get release, u may have court document & in that kind of case you'll be fine with a good lawyer.
but if you manage to enter otherwise i guess you have 2 possibility
1-your wife has a kind of status: she will apply as the main applicant and in the appropriate box put "NO STATUS" for you her husband and your case will be process in baffalo (usa) -but what i am worried about is the kind of charge they might have put on you when they caught you- need to talk to a lawyer please!
2-you apply & and get ready to return in your home country for interview if you were called 4 1.
i share your pain and pray that someone come up with a real solution to your problem...once again if you can afford a lawyer don't hesitate 1 second coz it's hard and painful to be illegal and i can't imagine how they live
Jah bless u
good luck