Mostly you'd simply see a renewal of the old Age of War - just Mark II this time round.
The game changer (at least regarding the Clans) would be the year of peace rather than the type of peace proper.
So say, this peace took place right after the 1st Succession War then it's very likely the Clans would be in a terrible position no matter when they finally decide to invade. Not only is additional infrastructure saved from the predations of war and time, but economically, the Successor States are less hostile. Comstar would likely maintain Terra & the HPG network, but be far less religious and militant. Toyoma's changes wouldn't take hold and his successors would have a hard time (if they opted to maintain the pseudo-religious trappings) recruiting manpower. Remember, Comstar recruiters preyed on the anxieties and realities of the Succession Wars. If things improve and total warfare ceases, Comstar's recruitment dissolves correspondingly. I'd put money on Comstar going completely corporate, but build a corporate model resembling Shadowrun's Aztechnology, i.e., plenty of skeletons in the closet and mighty good at public branding/propaganda.
Still, even if said peace took place after the Second Succession War, the Great Houses still benefit from another 150+ years of their own brand of ritualized warfare. Technology, commerce, everything the Third Succession War helped stagnate would benefit. Again, Comstar would suffer the worst if it maintained their canon model, which again, I doubt would happen. Within a certain period of time it's not a stretch to imagine another Second Star League forming much like it did after the Clan invasion - albeit this time without the need for or reason of a common enemy.
Why? Because if the Great Houses can sign a peace accord on their own without a common foe bearing down their neck, it's not implausible said Houses could also come to the same Second Star League agreement. If you're willing to deal for no apparent reason other than common sense, then you're probably likely to deal in the same fashion again.
You should also take into account time and generation. In 2864 there were probably still people (albeit advanced in age) who still remembered living in the Star League or during the waning years of Sphere-wide peace. If a peace occurred in 2864 there are still people alive who could call upon the actual memory of cooperation and its benefits. If their leaders were willing to play ball, so would they.
In 3058, no said generation exists. Cooperation without coercion (in the form of the Clans) was impossible. Those people would have 250 years of constant warfare, with successive younger average generations to correspond with the declining technology. (Take Terra for example. Even in 3078, Terran don't reach middle age until well past their 60s. Medical technology and health means Terran generations are further apart since women care bear children at a more advanced age. The same can't be said for a place like Philadelphia or Helm, where successive generations were born closer and closer to each other - say, 20 years apart rather than 60+.) If a college or technical school provides a form of institutional memory, what kind of cultural memory is passed from parent to child?
It's a rhetorical question of course, but highlights the idea that some of the ingrained stigmas of the Succession Wars may not be fully solidified just yet.
Again, operating under the assumption of the Alt-U you've created here, it is possible.
