Regardless of how they are obtained, they are still dice results. So, if one plays a card to obtain two Groo Heads, one can use the Pawnshop to convert them into a Kopin. We play that Groo destroys any Shipyard that pre-existed when Groo came to town. There are two types of such effects. Optional effects are powers that the player may invoke, such as the Pawnshop's ability to convert dice or the Wizard's Keep's extra turn.
Mandatory effects begin immediately upon playing the card.
Optional effects cannot be used the turn the card is played, but can be used during the next player's turn. A variant with two or more decks will be interesting, I think. With the expansion set, adding this rule is a good idea. Players replace starting with the phasing player and continuing clockwise. This may make some events' durations very short.