Nope- the Navy has seized F4F Wildcats and such that were recovered from the bottom of Lake Michigan without permission. The folks that found a rare TBD sunken in the ocean probably still haven't revealed it's location for just such reasons.

I have seen more than one 1911 rendered down for parts and the frame destroyed when brough for sale to a gunshop. Law enforcement is usually handy and they make the call on the weapon's disposition.