Yes, you can absolutely activate a creatures ability before it dies, assuming that you can pay the costs
Getting them in unblockable will melt life totals, and if anyone is shields down, they might have to eat some double strike, too
However, if Duggan leaves and later returns to the battlefield, he's considered a new permanent (with a new set of abilities) and it can be activated again
Those who grew up playing Pokemon cards probably remember the incredible awe one felt when looking at a super rare cardmaybe a Mewtwo or a holographic Charizard
These cards are both collectible and playable, and since character Cast Members all learn the signatures of the character they play, there should be a uniformity here for collectors, no matter which park's characters might be signing
Some local game stores may also have extra bonus cards or sealed drops in stock