If a listing says "Engine Starts," does that automatically rule out driving it afterward?

Not necessarily — "Engine Starts" only confirms the engine turns over and runs. It doesn't confirm or deny whether the vehicle can be driven; that's a separate field ("Runs and Drives") that may or may not appear depending on whether staff tested it further. If you only see an engine-start confirmation and no drive-tested status, treat drivability as unverified.