Not in military terms, of course-- but in political ones, absolutely. The Republic's stated victory condition was simply to force Manticore to the negotiating table, and to get an honest peace treaty out of them. And by those standards it succeeded brilliantly.
Not only did they succeed in obtaining a peace treaty in a far shorter time frame than the first go-round, but it was undeniably a far better treaty than they would have gotten from High Ridge. Hell, it was a far better one than they would have gotten from Cromarty!
And I would argue that outcome would not have been possible without the war, and moreover, without the war exactly as Theisman conducted it. Most obviously, the extreme contrast between the way the reborn RHN acted and the actions of the PN set the stage for the people of the SEM (not to mention Elizabeth) eventually being able to accept that the leopard had changed his spots back at last.
But it's also possible that a conventional opening campaign would not have led to the treaty and the GA at all. A slow opening, to an officially-announced war, with fewer losses for the SEM, might not have brought down the High Ridge government. Elizabeth would have hated them just as much, but if they could have ridden out the first shock, who's to say how much longer they would have held on? At the very least, their goals and hers would have coincided as far as the SEM's survival was concerned, and they did have the Salamander at their disposal. And that would have led to truly dire things for the SEM, had High Ridge been at the helm for Monica and the conflict with Mesa and the League.
Not only would Pritchart have been out of her mind to trust him as far as she could throw a SD(P), it's highly unlikely that High Ridge--who didn't even trust his own allies-- would have supported any attempts Elizabeth made to come to an arrangement with Haven that didn't let him maintain his power somehow. A treaty of mutual defense, with technology-sharing, etc? Forget it.
And last of all, by very nearly defeating Manticore militarily as well, Haven proved it's worth *as* an ally. Without the second war, even the most cautious, like White Haven and Honor, are left still viewing the RHN as they did the Peep navy previously: inferior tech that's now even more outdated, inferior personnel, little ability to innovate-- "like pushing baby chicks into a pond" as Hamish put it. Thunderbolt put paid to all that.
I won't argue that anyone in-universe views things this way-- even if they might have, I suspect the truth of Giancola's manipulations overshadows everyone's thoughts on the "rightness" of the war itself, and it's personal costs (especially to Theisman and Pritchart) probably prevent them from viewing it with anything but regret.
But at the end of the day, the Republic of Haven fought as honorably as they could on the best information they could, and regardless of how the Battle of Manticore ended, the Republic achieved exactly what they set out to achieve: a peace treaty that let them maintain the gains they had made in restoring the Republic's soul, with a path forward to regaining the trust of the galaxy, and a little leg up on those tech problems.

At worst, given that the SEM's victory condition was basically "just don't lose", you can say it was a draw.
