Waive,
I don't really know the motor vehicle laws in VA, but I do know them very well here in PA as it is indeed a requirement for the profession which I am in (guys: no cop bashing now). Cops, or at least a vast majority of them, do indeed know the rules as they apply to antique and/or classic plates, however, as DaDon, Gator, and DZauto have replied, they are for the most part exactly correct in that if you do "push it" and give them a reason to bring you down, they will. If you just use a little common sense and do not draw attention to yourself by doing things that you really shouldn't be doing on the streets, you will not have a problem. However, if by chance you do get stopped for whatever reason, don't lie to them. Being honest with the law goes a long way in determining the outcome of the stop. Don't give them some spur of the moment made-up excuse that really can't be substantiated because quite often they WILL check into it.
On the other hand, here in PA, having a permanent antique or classic plate technically has nothing to do with the inspection of the vehicle. It is nice that you do not have to worry about renewing your registration every year, but you still must technically comply with all inspection regulations in that the vehicle must still be anually inspected. Even in PA, would you have a problem with not actually having a classic vehicle currently inspected...probably not. Unless you pushed your luck by doing something else that you shouldn't have done in the first place.The law looks at a vehicle with classic or antique plates as being a "Sunday driver" car. This means to and from shows, repairs, parades, weekend drives, etc. I don't want to give you the idea that such are the only times it can be driven. I will often hop into one of my father's classic Triumphs (with classic plates) and just use it to run to the store or whatever. It's not a problem unless you're using the car as an everyday driver; and believe me, the cops will pick up on it if you do (especially in a smaller town or city). You will probably get more of a hard time from your insurance company if you obtain special rates for your classic car and they find out that you are using the car for every day use. A little bit of common sense goes a long way, and most cops have that too.