I kind of agree with everyone else - call the agent to be 100% sure, but at least in NY the insurance is kind of on the driver and the car. I.e. the owner of the car is covered by their insurance whatever car they're driving, and their insurance covers their car whoever's driving it (though perhaps not liability for the unauthorized driver). If you're going to drive it more than once or twice a year however, it's probably safest to add you as a named driver, which will increase the insurance costs in NY unless you had your own insurance policy (that you can only get if you own a car). But then you're explicitly covered, always a good idea IMHO.
Edit: In general it's always best to talk to an agent to be sure what your policy covers. I found out NY recently passed a law where everyone has to have an extra cost policy to cover their spouses unless they specially opt out. I'm not against covering whatever that was intended to cover, except for the fact I'm not married. I don't like paying extra to cover a non-existent person that the state apparently assumes everyone has. I won't even get into the inappropriateness of that assumption given current marriage and divorce rates.