maybe if they pulled you over for no reason... but you're out on roads you don't own, driving a car around with a big number on it that everybody can see.
but you don't own your plate, that government does. long story short, they can do with their own plate anything they want...
as far as what's been decided previously, RI v. Bjerke, lady calls the cops about a drunk driver and give cops the plate #, cops then go to that area and see the car with the correct plate#. and without waiting to see him actually break a law, they pull him over right away and arrest him because he's wasted, he appeals saying that they had no right to just pull him over based on a plate number
“In considering his contention, we point out that a Fourth Amendment search is only involved when the government intrudes into areas in which an individual is said to have a reasonable expectation of privacy. This expectation of privacy must be actually held by an individual and must be objectively reasonable.”
In rejecting Bjerke’s argument the court concluded: “We do not believe that either Bjerke or the public at large has any reasonable expectation of privacy in a motor vehicle registration license plate. We reach this conclusion in view of the fact that such plates and the information behind them are within the control and custody of the state through the Registry of Motor Vehicles"
another side to that is cops can't search your car for no reason, but if they see something in plain sight, then all bets are off. well plates are in plane sight.