According to federal mandates, the unemployment system puts collected tax money in a general pool. If you were a covered employee (or were supposed to be a covered employee) then even if your employer was not reporting your wages paid quarterly to the state unemployment system you will be able to draw from this general pool.
That is not to say that you may have some issues and delays at the beginning. You need to be sure and file your claim the first week you are out of work. Don't piddle around and wait to see if you find anything else quickly. You look for the new job after you file the claim. When you file, be sure you have check stubs, W-2's, proofs that you worked for this employee for the time you did work there. Don't be surprised if you apply, and they say, "You don't have any wages to set up a claim" on your first monetary determination.
The quarterly wage reports made by the employer are used when the ss# of the claimant is plugged into the system and if it works as it should, the wages they have been paid in the appropriate quarters and the amount they will be able to draw will come up in the system. But if your employer hasn't been making these reports and paying taxes as they should, this may not work for you.
If you get a monetary determination that says you are not able to draw benefits or shows some quarters in which your wages are not reported at all, you will immediately need to appeal this determination, and show them that you have proof that you did work for the employer as a non-contract employee and that you were paid thus and so. Then wages will be assigned and a claim will be set up for you, the money coming out of this general fund, of course. You will be able to begin drawing. You will have been certifying for each week you were unemployed after your claim was filed, so even though it may take a week or two or three to get it started, you will eventually be able to get benefits.
You won't even know about it when the state goes after the employer, but they will. It's not a matter of you "making it worse" and it wouldn't help a bit even if you decided not to sign up on unemployment all together. As you said, they're already after him, already trying to get this situation resolved. It's not that you separated employees are sigining up on unemployment that is the problem, that this employer was not paying his taxes on any of his employees, and that's something that will come up between him and the state unemployment system even if they never laid anyone off and no one ever drew unemployment who'd worked for them.