No, normally if someone not on your policy drives your car his car insurance would not cover your vehicle if he caused damage to it when operating it.

Generally car insurance works as the car owner's policy being primary and the driver's policy being secondary or excess. So if the person you loaned the car to was in an accident your insurance would be used first and his insurance may be gone to if your limits are exceeded, however this usually only pertains to liability insurance and not physical damage coverages of collision and comprehensive.

"Full coverages" of collision and comprehensive usually do not follow a driver to other people's cars that he may drive. This makes sense if you think of a person that is paying premiums to have full coverage on a Ford Escort that borrows a friend's pricey Cadillac Escalade and wrecks it The premiums that the driver has been paying for collision coverage on his Escort would not be the same as the Cadillac owner and thus having his insurance pay for a much pricier car to be repaired would not be something that an insurer would want to do.

So if a friend borrowed your car and crashed it, then you own insurance coverages would be used to fix the vehicle, not your friend, the driver at the time of the accident.