Yes, normally even if your insurance was expired and the driver of your car was also uninsured you can still place a claim with the at-fault party of your accident for the damages your vehicle sustained. You would place the claim through their property damage liability policy usually.
If your vehicle is determined to be a total loss (written off) then you may be able to use your GAP insurance, but you will need to read over your policy and ask your GAP insurer if your GAP policy would pay out without you having primary insurance of collision and comprehensive on your vehicle. Insurance policies differ so that is why you need to find out this information directly from your GAP insurance carrier.
When you either get your vehicle repaired or a new vehicle to drive, make sure to place insurance on it since driving without insurance is typically a serious offense in most states. You can get an affordable automobile insurance quote here with us.