Givin' this thread an update in case someone needs this info:

After several months of sweating bullets and wondering just what the clearance process might dig up, I finally received my FBI clearance letter. The letter did NOT say anything about my immigration status, just that I don't have any arrests on record. I just submitted my fingerprint card and a cover letter, and I didn't even provide a SSN.

So I guess I'm either home free or ICE is going to bust down our door anytime soon.