Had a conversation with someone previously and I'd just like to get these in writing so they can be posted as rulings on the card descriptions in the future.
Teamwork: "After edge stacks are revealed, you gain +X force icons for your side for this edge battle. X is the number of different affiliations among cards you control."
Gladiator-class Star Destroyer: "While this unit is participating in an engagement, it gains,
'Reaction: After your edge stack is revealed, place 1 card not named Twist of Fate from your hand into your edge stack.'"
To my knowledge, if you go into an edge battle and both players pass without throwing cards in you can still play Teamwork.
BUT, you could NOT put a card into the edge battle in that same scenario using the Gladiator's text (assuming he's participating in an engagement).
Also while I'm on the subject of the Gladiator, it is to my knowledge that you can't trigger Inexorable Destruction off of its text, correct?
Inexorable Destruction: "After you reveal 1 or more [Imperial Navy] fate cards in your edge stack, target a participating friendly enemy unit. That unit strikes immediately."