Does a check invoke a trait if the actual character making the check has that trait? (For instance, someone playing one of the goblins using the Magic Pig).
A check invokes a trait if it has or is against a card that has that trait. A card invokes a trait if it has that trait. A bane also invokes a trait if it deals only damage of the type that matches that trait.
In other words, no. The traits on the character making the check have no impact as to whether or not the check invokes a trait.
Whenever you make a check, you don't add your character's traits by default. So, for example, when you make combat check with goblin character, you don't add "goblin" trait to a check, so you don't invoke "goblin" trait.