No, they are not going to make you pay back benefits with one hand and then hand over benefits with the other. That doesn't even make sense.
I was not diligent in keeping records of my part time job hours when collecting unemployment a couple of years ago. I wasn't deliberately doing this - I was shocked to be abruptly fired from a job that I'd had for over 14 years.
So, they cut off benefits and I had to repay the entire amount that they overpaid me, which was entirely correct. I didn't mean to not keep accurate records, but I should have been more diligent. Lesson learned.
If you are ever eligible to receive unemployment benefits again, your account will probably be audited to the nth degree to make sure a mistake doesn't happen again.