Egwene now consider what she had to do a "necessary evil" - that the end she sought justified the means, but that it didn't make them any less harmful to the good of the Tower. Now that the Tower is reunited, she seems ready to play by the political rules within the system of check and balance.

We don't know enough about the Law of War. Technically, if it could be proclaimed against an entity like "the Shadow", the Tower would have been perpetually at war since its founding... it rather seems that the fight against the Shadow is part of the Tower's traditional mission and doesn't call for any formal declaration of war. Declaring war against the Shadow might sound a little stupid... make it sound like the Tower wasn't fighting the Shadow until then.... that might remind people that indeed the Tower was too busy with inner fighting lately to do its job...

It sounds more likely that this law was introduced after Hawkwing assieged the Tower and targets nations or groups like the Whitecloaks that might fght the Tower one day.

Deane Aryman who apparently was doing a spectacular job at rebuilding the Tower after Bonwhin died too early trying to negotiate in person between factions in the War of Hundred Years. That was probably considered a disaster. That's possibly the occasion after which the Hall made it law that the Amyrlin could not willingly place herself in danger without the Hall's pre-approval unless the Tower was itself at war. It would explain why the Sitters were so unfamiliar with this law: it would be an obscure Law that's never been used except to stop Amyrlins from placing themselves in danger (Sitters tried to use this to stop Siuan from going to Fal Dara in TGH, but they lost the vote). The rest of the Law, concerning the leadership while at war, may be very little known (it sounds like the cookie handed to the Amyrlin in the most unlikely case the Tower went to war, in exchange for placing a limit of her power all the time. The Hall had to convince the Amyrlin to sign this law...)

The bigger question is whether the Hall will or not want to declare war on the Seanchan or consider that they must because the Seanchan are de facto at war with the Tower already. If the bloodknives continue to kill sisters, the Hall may realize the danger is far from over.

But I doubt if anything like this happen the initiative will come from Egwene. If the Law of War is enacted again, that will be at the initiative of the Hall itself, IMO. It would hinge on whether the Hall believes the Tower benefits from giving Egwene special powers to prosecute the war against the Seanchan, or if the Hall can work well enough to keep running the Tower with the Amyrlin the normal way. I think some Sitters would call for the Law of War only if the Hall is so divided again that swift decisions about the Seanchan just can't be made, and for some reasons I doubt the Hall will dare stalling and bicker over everything again for a while: they too have their lesson from the Tower split.

Personally, I doubt we'll see much of the Hall in the rest of the series. Egwene is supposed to have only a few chapters in ToM. Last summer, Brandon was expecting Rand and Egwene would get about as many chapters in ToM as Perrin and Mat had in TGS. This means we will see far more of Asha'man/Aes Sedai in secondary plotlines and outside the Tower than we will see the White Tower events. The Egwene chapters are supposed to be a bridge to the book's final section, when the main characters reunite at the "event" that marks the beginning of TG proper.