It's not a bad idea, at the core, and I don't think she would necessarily have to die to make Gawyn upset; Warders have been known to go at least a little berserk for less. I have been putting some thought into the possibility that Egwene would die, and not bond Gawyn, but it doesn't seem to work with other prophecies. If Egwene isn't going to be saved by Tuon until after Rand's death, then the confrontation between Egwene and Rand where (presumably) Tuon is there can't happen until after his death (and resurrection). Of course, there is a possibility that Rand and Egwene will chat before he dies, and that the Seanchan woman with her is not the same as the one with the sword that saves her (Tuon). In that case, it might possibly be one of the Bloodknives, or Alivia (though it would be weird for Alivia to be 'with' Egwene rather than Rand), or Egeanin (who knows Elayne and Nynaeve well, of course), or maybe one of the sul'dam with Mat. This has interesting possibilities, actually, because Seta was one of the sul'dam that often held Egwene's leash, though Renna was the one that captured her and held her leash most of the time (and Mat ordered the arrow that killed her in Crossroads).

Anyway, the woman with the sword is still most probably Tuon, since Egwene also saw herself linked to a female hawk that stretched its wing to touch her. That could be Berelain, but Tuon seems more likely, since she'll be getting Justice (while the woman's face wavered, the sword was solid, which places extra emphasis on the sword).

So, if the woman in the confrontation dream isn't Tuon, then there is still a possibility that Egwene will die or be in some way seriously wounded to trigger Gawyn attacking Rand (especially if he knows that Rand and Egwene met around that time, and is able to believe that Rand had something to do with it). Of course, it will probably be Mesaana, or something related. Maybe Egwene will die and Siuan will be Amyrlin again. And all the Egwene-haters will rejoice. *sigh* But then, how would Tuon save her? Maybe Gawyn will actually kill Rand in Tar Valon, and it will just happen to be more or less simultaneous with the Battle of Caemlyn (they're not exactly related, though there are some things that could easily make them related). That way, the sky above really would immediately go dark as Dragonmount blows. And I wonder how long it would take the ash to get to Caemlyn....

Finally, in case you can't tell, I don't really have a lot of solid ideas on the details of what is going to happen. I didn't feel the need to plot it all out when I posted the theory. I do like brainstorming on it though, and every now and then, something resembling evidence pops up, and the big picture gets a little bit clearer.