With or without her, there is zero possibility that the Tower would have been enslaved. They were RAIDING. They came to grab as many mareth'damane they could fit on the backs of their flock of to'raken and fly home, while causing as much damage as they practically could. Slaughtering every person on the premises they did not carry off would only have resulted in the death or chaining of no more than a quarter of the Tower, maybe 30% at worst. There would be an absolutely majority of the Tower surviving, consisting of hundreds of Aes Sedai, at least one organized body capable of electing an Amyrlin, and the overwhelming majority of novices, including many of the strongest and most promising. And that's a worst case scenario.

Egwene no more saved the Tower in that incident than the most heroic NY firefighter saved the city on 9-11. Namely, she did not, at all. She did a bunch of damage control, she saved some lives that might otherwise not have been saved, she was in position to do ANYTHING because of the fortuitous bubble of evil transposing her quarters to the actual Tower itself, and she committed inexcusable murder along the way, that is actually much worse on her hands, considering her own presumption to lecture others on violating the Three Oaths, or assuming the guilt of people she has not seen in months. I will grant that the murders in question might simply have been Sandersonian imbecility, but as depicted in the book, they were exactly that.

Saerin actually displayed greater leadership during the crisis, while Egwene herself would take steps to ensure that no one could do what she did, by stashing the -greal where no one else could hastily grab them in an emergency.

The irony is that the greatest harm of the Seanchan raid, which made the whole affair a resounding success according to the parameters the set out for the mission in their briefing of Tuon, was due entirely to Egwene's blunder making Traveling available to the loyalist sisters, and the Seanchan capturing Elaida and gaining her knowledge themselves. That alone would make the proposed raid a success, according to the Seanchan mission brief, and they got it.

Egwene used a whole army of people to fight Mesaana, including three women who claimed greater skill in T'A'R than the Forsaken (at least one of whom embarrassed Egwene herself during the fight), and she only succeeded because Perrin dumped the dreamspike there, otherwise Mesaana would have E&E the way Egwene assumed she would in terror of Egwene's arrival in the Tower as the real Amyrlin Seat. It's an accomplishment to be sure, but hardly impressive coming so late after Nynaeve, with less training and fewer allies, defeated her more formidable compatriot. You yourself acknowledged back then that she won because she was so firmly fixed on an errant idea.
It was a battle. Someone would have done for him at some point or other (especially if they had the opportunity to go after him with one of the most powerful sa'angreal known to exist) and all they did was throw power at one another. From another point of view, if Egwene is all that her fans make her out to be, M'hael came out ahead in that fight, since he removed an indispensable piece from the roster of the Light, at the cost of a minor & inexperienced Chosen. The weird thing is the emphasis on killing M'hael, when countering the balefire effect would count, I would think, as much more significant and impressive. Had she found a way to do so safely, that might have finally been a One Power feat to rank with Nynaeve's Healings. Her willingness to destroy herself because of her own sufferings degrades the nobility from the achievement, however.