Yes I can, because I have that exact type of coverage on my policy. Where I live, it's officially called OPCF 27, and it extends my Collision and Comprehensive coverage to any private passenger vehicle I rent.
NOTE: While I have that coverage on my policy, and it's valid from coast to coast, a rental company cannot be forced to accept it. The owner of the vehicle (the rental company in this case) is allowed to set their own rules governing who can and can't drive their vehicle.
But you don't really need to know what my auto policy covers, you need to know what your policy covers. The only place you can get that info is your insurance provider, no exceptions. So give 'em a call and ask.