First off I am not a lawyer but I've dealt with our state unemployment agency quite a bit in the past two years.

If I understand you correctly, you were collecting benefits (i.e. saying you were "unemployed") while working under the table, and not reporting those earnings? Well that's trouble right there. You were not entitled to those benefits and the state could prosecute you for fraud (and require repayment plus interest). So, I'm not sure why you would even think of disclosing that information.

Now perhaps the work and the UC were at separate times (i.e. no fraud)... OK. Most states base benefits on earnings, which are verified with the employer.
Let's say you file a claim and report those earnings as wages. And then the employer responds that no, you were an independent contractor. In my state we have the right to dispute that classification. In that event, an Employment Security staffer will resolve the dispute using a 12-point test. Many times, a claimant will be re-classified as an employee for the purpose of UC benefits. You may very well be able to do that.

Things to consider first however:
1) The employer might get in trouble for wage law violations. Don't expect to be re-hired there in the future.
2) You may be liable for taxes on that income, penalties for failure to report, etc., depending on who talks to whom. In fact, you are already guilty of failure to report and pay self-employment tax. The IRS takes a very dim view of this.

Therefore, make sure that those earnings, if counted, would actually help you establish a claim. Sometimes they aren't enough to make a difference and then you can skip the whole exercise.
Personally? I wouldn't go there, because you're really as guilty as the employer and you both stand to lose quite a bit. Good luck, hope you have found a new job by now.