Certainly could cause you problems to do that. DMV can prevent your vehicle's registration renewal or even suspend such registration, until you are in order again. If that's your case, please take a look of local Traffic Courts.
Hum,  got it. Lastly, there is any special situations about vehicle registering in NYS?
Sure, there is. DMV has some topics under the special situations tag. There is special procedures for agricultural and farm vehicles, homemade vehicles and trailers, or the sad situation of an deceased owner.