It depends on a lot of details, and you didn't give any. Let's pretend the suspended driver is me, because I have a vehicle with valid auto owner's insurance on it.
If I lose my driving privileges for any reason, any reason at all, my policy won't cover anything while I'm driving. Auto insurance contracts all have a clause in them that says the driver must be "authorized by law to operate the insured vehicle", which means they don't cover drivers who don't hold a valid licence. And they're serious about that clause.
But if my wife is driving, with her valid licence, they'll cover that accident because her licence is good.
But you specifically said driver's policy, which is actually a type of auto policy of its own. And no, a driver's policy (also called a non-owner's policy) won't cover you if your licence is invalid.