I thought that was mostly later though after they'd run out of good terran targets to go after?
It was a semi-back and forth thing for almost every participant, to one varying degree or another. That's how you explain Towne for example. Every Successor Lord sent troops into the former TH, but the amounts varied. Fronts between states also went from hot to cold during the war.
Sticking to canon in this "what if" might only work for the Lyrans. For example, if Minoru does sack Avalon and kill the ruling Davion line do you really think the Capellans will restrict the fighting along the Davion border to heavy raids, or would it embolden them to fully invade the Capellan March? Ya know, blood in the water and sharks, or a piece of the pie, etc.
In turn, how would that change the war along the Free Worlds/Capellan front? What about the Periphery? Would the TC feel bold enough to reclaim some historically owned worlds? If so, how does that change the little fighting between them and the MoC?
Finally, what about the Combine? Taking New Avalon and killing Prince Davion puts the Coordinator at a crossroad. Aim for the Hegemony to bolster a claim for First Lord? Invade the Commonwealth? Consolidate the Federated Suns by continuing to invade?
Where does ComStar fit into this? The brutality of the First Succession War an exercise in pointless. There was virtually no gain, just loss and the ranks of the participants remained stagnant. Knocking the Davions out changes the board. Does ComStar approach Minoru? If he reasonable enough by their standards? Does ComStar wait a little longer, see what the Combine does next before making a move? Or do they immediately go into secret counter attack mode?
Again, how far along in the storyline, how much you change in canon should help determine these answers. Blake knew the Council Lords were arrogant, selfish idiots who would probably drown the Inner Sphere in blood to claim the throne. The start of the First Succession War proves that. However, he also styled ComStar after old orders designed to survive "Long Nights." Yet, ComStar is in its infancy. It hasn't had generations to solidify its doctrine, or consolidate Terra and her secrets.
Blake may very well have disliked all of the Council Lords, but he loved the Hegemony more.
Conquest, if truly accomplished, of the Federated Suns could be a tipping point depending on what Minoru decides to do and accomplish next.
