I was a part of an intense discussion on this issue in another forum. In short, I believe we're going to have to wait on a definitive ruling, but I have a strong suspicion that the devs/rules team will eventually rule that yes, TIE Attack Squadron receives its bonus even if the edge battle is cancelled.
The conditions precedent (requirements) for the bonus modifier on TIE Attack Squadron are:
a) most obvious, it must be in play and unhindered by any enhancement/effect that would preclude the effect;
b) it must be "during any engagement," which specifies when the bonus can occur and establishes a limit for the bonus duration;
c) at least 1 fate card is placed into an edge stack. <--- Therein lies the point of contention.
I can think of two ways in which it could be justified that TIE Attack Squadron keeps the bonus:
1) The devs/rules team define cancelling an edge battle in a way that does not mean that cards placed in the edge stack of the cancelled battle were not placed. For example, they could say an edge battle that is cancelled is simply not resolved, but the process of having placed cards in that battle remains unchanged. The argument that TIE AS does not receive its bonus hinges on declaring that the entire process of the edge battle cancelled by the Twist of Fate is thrown out altogether and treated as if it never occurred.
2) The devs/rules team rule that cancelling an edge battle does imply that it basically never took place at all, BUT they consider "placed at least 1 fate card into the edge stack" a condition precedent satisfied by a singular occurrence (basically, treat it as a cost) as opposed to it being one capable of continuous verifiability (like "during any engagement). In that case, the instant a fate card was placed into an edge stack, all conditions were met, bonus applies, and that particular condition precedent (placing of at least 1 fate card) is never reassessed (think of it in the way you play cards; once you pay resources for a card, you can't unpay them no matter what else happens in the sequence).
Again, I'm in wait and see mode on this one. Currently, there simply isn't enough evidence to make a determination one way or the other so far as I can tell.