If I play Curse of Threes will Tarrison's effect still trigger?

Yes, Tarrison's effect will still trigger. While Curse of Threes is still an active crew member when on top of an opponents' deck, the Curse of Threes does not count as being apart of the crew of either player. The Curse of Threes is considered its own crew member of a some spiritual realm, and a sidekick to an unknown entity. The card is still owned by the player who played it, and will return to their discard pile once discarded.

If an opponent plays Curse of Threes on you while you have Tarrison as your only active crew member, Tarrison's bonus would still trigger. If Tarrison's bonus is successful (by rolling a 4,5 or 6 with 1 d6) then you would still need to roll for Curse of Threes (by rolling 3 dice) to see if you draw the extra card.