I bought the Pirate Seas Pack and it looks like once you unlock the ship it stays there, so I was wondering if I traded my ship away if that would matter? Potentially I could trade with someone that bought the other level, the something-or-other crypt.

Anyone know if this is possible?

Technically yes, I believe the Adventure level unlocks are tied to your individual savegames, but that means that if you start another playthrough and/or erase the previous savegames then that level won't be available. I think the PvP arena unlocks are tied to the console itself instead of the savegame, so you won't need to worry about that aspect.