Whether it was that way originally or simply the result of events Latra seems to have led the women and LTT the men at the end of the War of Power. I've personally always thought that was a schism after she refused to participate in the plan to forge the seals, in preference for her own doomed plan to use the Choedan Kal (though it's never quite clear how they were to be used, even had the areas where the access keys were created not fallen to the Shadow). In other words, I think LTT initially held overall leadership of all channelers and Latra only rose to lead the women when so many rejected LTTs plan to end the war. If that was the case, while there may be a male and female leader similar to what the Ajah Heads and Sitters provide, I only anticipate one supreme leader in a TRULY reunited Tower.

However, there's no way to be certain, and even if I'm right about the history there's no guarantee the future will unfold identically (though I think it would function a lot more smoothly; there's enough intrigue and conspiracy in the Tower without granting the highest authority to TWO people rather than one and then restricting that authority to the respective genders of each). In that case having to deal with Logain as an equal would undoubtedly be a humbling and, one would hope, edifying experience for Egwene. If nothing else though, I think it's unlikely as long as she insists on Aes Sedai swearing the Oaths; Logain and the other Asha'man don't strike me as the type to potentially give up half their lives just to satisfy the pointless custom of women who tried to hunt them down and kill them. Of course, if Aran'gar does have some lingering influence over her perhaps that rare example of Egwene reversing herself in a big way wasn't really her decision in the first place.