AFAIK you can't make a whole PCB (printed circuit board) out of gold only as for the conducting parts, including traces.
Even if connectors wouldn't corrode, traces and chip legs would.
Surface-mounted legless chips would be less vulnerable to corrosion but I don't know if FDRs/CVRs have that kind of technology. Aviation electronics tend to lag behind and stay on the less advanced / safer side of things.
Anyway, they could always unsolder the non-volatile memory chips and put them on a dedicated reading equipment. To my knowledge, this has been needed several times in the past to read out data. It just takes more time. I'm fairly sure that advanced facilities have a way to even get to the dice inside chips and pull data from them.