The idea behind Quickdraw is to use Elusiveness and Electronic Baffle interrupt an enemy ship's attack, hopefully destroying it. This is not covered explicitly in the current rules, but based on the timing chart I think the enemy ship could be removed from play before resolving its attack against Quickdraw. I tried to post something about this in the Rules forum, but I'm new and the moderator hasn't approved the post (yet?)

Snoke's Blokes (100)

"Quickdraw" (32) - TIE/SF Fighter

Elusiveness (2), Electronic Baffle (1), Special Ops Training (0)

"Omega Leader" (26) - TIE/FO Fighter

Juke (2), Comm Relay (3)

"Omega Ace" (23) - TIE/FO Fighter

Push The Limit (3)

"Epsilon Leader" (19) - TIE/FO Fighter