Is it illegal to claim to be illegal immigrant?

Great question, but really, I don't see how they could prosecute you for it, but then again how would you be able to credit the education to yourself without spilling the beans and admitting that (unfortunately) you're here legally. I think it'd be worth trying though,....once you've already got the education, you can straighten it out then. Best of luck with your scholarly pursuit. Even legal residents should be able to get an education.