No, your Gap insurance would not pay your Collision deductible for this accident where an uninsured motorist damaged your vehicle.

If a covered loss occurs, GAP insurance pays the difference between the actual cash value (ACV) of you vehicle and the current outstanding balance on your loan or lease. Gap Insurance protects your vehicle lease or loan in this way. Sometimes it will also pay your regular insurance deductible however this is only when you car has been totaled out, not if your car is going to be repaired.

If your vehicle has been totaled by accident, theft, fire, flood, tornado, vandalism, or hurricanes your insurance company typically pays the ACV. It is often considerably less than the actual amount you still owe on your loan or the amount due for a lease payoff. Gap insurance then is used to pay that remaining balance and in some cases will also pay your deductible but Gap insurance is only for these total loss situations.

In your situation it appears you are aware of who the driver is that hit your parked car since you are know that this person is uninsured. If that is the case than you may want to seek legal advice to see if you are able to sue the person in court for your deductible amount and any other expenses you are out due to him or her hitting your car.