So it is Gawyns fault she jumped to a false conclusion? Is anything ever Egwenes fault? Say we go with your premise: Her warding captures the first Bloodknife, his colleagues do not stick a knife in him on the spot to keep him silent (as (probably) Sheriam did with the Gray Man in the Tower during Egwenes first residence) and the Tower takes him prisoner. Assuming he does not have and use a suicide pill, are you asking me to believe she could and would break sufficiently break him with interrogation to reveal there were still others lose in the Tower? Or is it more likely that his capture would simply convince her he was a lone wolf, a straggler from the previous raid who did not make it out when the others fled? After all, Egwene still thinks that raid was a fullscale assault (which is why the ACTUAL assault will almost certainly catch her completely by surprise and unprepared.)

The problem with expecting her to react rationally and logically if Gawyn did not interfere is that its belied by her habit of reacting irrationally and illogically on that and so many other occasions. She KNOWS she screwed up with Gawyn, both in behaving in a way that drove him away and in forbidding him (essentially) to save her life, errors so grave they almost killed BOTH of them. Do not hold your breath expecting her to admit either to him though; she has the benefit of "Amyrlin Infallibility." Or maybe just "Egwene Infallibility;" previous Amyrlins have repeatedly and indisputably erred, but THEY were not Egwene.