If they didn’t eat oysters it would have been because they didn’t want any. The Jamestown settlers first landed not far from Lynn Haven Bay in Virginia Beach.
This is an area near where the Chesapeake Bay flows into the Atlantic. I would guess that it would always be very close to sea level regardless of drought or not.
I forgot to mention that Diamond Jim Brady preferred Lynn Haven Oysters to any others.
Alas, the inshore water, and that includes the Tidewater James River, would be brackish so all seafood would tend to the salty side. With no local source of fresh water, they’d soon died ~ which, in fact, is what happened at Jamestown!