I think that's a dicey game. You might be able to get away with it, or you might get caught someday. Essentially you must register your car in your state of residency, and real estate ownership has nothing to do with residency. A person can own houses in all 50 states for that matter, but is legally only a resident of one state at any given time. That's the state where you reside the majority of the time, acquire your driver's license, and register to vote. Those three factors (among others) is the threshold for most states to consider you a legal resident of that state. Again, ownership of real estate is not.
Legally, you must insure and register your car within you state of residency. AD military have separate set of laws and regs regarding residency we have to follow.