No, you could not claim against the insured driver's insurance. While he may be insured for his own vehicle since he stole your car his insurance would not cover him operating it since he was doing so in the midst of committing a criminal act (stealing a car) and thus obviously without the car owner's permission.

Also if he hit anyone else's vehicle with your car while driving it, as he stole it, they could not claim against your, the car owner's, policy since your car was stolen. As the owner of a stolen vehicle you obviously did not give the thief permission to use your vehicle and thus could not be found liable for that driver's actions in your vehicle.

If you know who the driver of your stolen vehicle was than likely your recourse against him will be to take him to court and sue him for the damages he caused to your vehicle while he was driving it as a stolen vehicle. If you have Comprehensive coverage on your own car you could instead place a claim with your insurance company for the damages and then they could subrogate against the at-fault party. This means after paying out for your claim your insurer would go after the thief that stole your vehicle to recoup the monies they paid out on the claim.

Your agent should be able to explain more to you about your coverages, how to make a claim and what your rights are in your state in this situation.