How old is the car?

I think if you don't have your car inspected, California won't allow you to renew your registration. But I don't think your current registration is affected by not having yet done the inspection. I am not positive on that, so don't quote me. But if I am correct, then you can still drive your car because your registration will still be valid. Next time you are back in California with it, get it inspected then.

No you can not get your car inspected in MA for CA.