Technically yes but given you are not really keeping your boat here you don't have to worry. They do collect data from state boat registrations so a VA registered boat is automagically taxed. They also collect from US documented boats based on the owners address.
No one will know and you really won't be staying at Waterside for very long. You need to exceed the time limit before they say you owe the tax. Just passing through on Jan is not a criteria alone. waterside only has transient slips any way so no one from the City is going to come around checking. Personal property taxes
are collected by the city or the county not the state. Norfolk is a city and there is no county. The state will collect a Use Tax if you keep your boat here after so many days. The tax is 2000 or 5.5% whatever is less and has nothing at all to do with personal property taxes
applied on boats, cars, trucks, trailers and RV's.
If you keep your boat at a marina for extended periods of time you do owe property tax and the use tax even if you are not a VA resident. That is true for all states that collect taxes. It is also possible to collect it if they can show you just moved your boat on Jan 1 to avoid the tax and brought it back. VA is sort of strict but FL and MD are very aggressive at it. They will actively search for violations. VA uses normal means available to the cities and counties to try and find everyone.