Mmm... that's a bit of a stretch. Engaging in asymmetrical warfare to liberate your own planet is a far cry from the sort of hegemonic empire-building that's implied in "Parallels"; even if the alt-Bajorans were not really doing that, and just involved in some sort of space piracy, they still had a ship that was capable of taking on a Galaxy-class ship, which suggests their having a way higher interstellar warmaking capacity than they'd had at any point in DS9. (Remember Kira shitting bricks during the standoff with the Romulans in "Shadows and Symbols" at the thought of having to fend off even one Warbird with the impulse ships that they had?) About the only way that the Bajorans could plausibly take on the Enterprise would be if they had somehow gotten hold of the Defiant, per the episode of the same name in which the Maquis did, with the help of... Thomas Riker. (And wouldn't that have been a great scene, if it had been part of "Parallels", with the two Captains Riker facing off.)

And yes, there was a treaty with Cardassia, but it's really more of a cold war situation, with the Cardassians trying to rearm in their very first appearance, and lots of other misbehavior (torturing Picard, for example) in the regular continuity. Combine that with their not even being seen until "The Wounded" and it's really unlikely that one would be posted on the bridge of Starfleet's flagship within a few years of the treaty being signed. Unless the divergence went something like this:

• Spock and Sarek don't have their falling-out over the Cardassian question (whatever that is, precisely), and work together to bring the conflict to an earlier resolution, in a way that favors a more moderate government--the Detapa Council, say. (That in turn would probably require some action against the Obsidian Order, and Spock could have been a part of that.)
• This, in turn, leads the Federation to be much more favorable to Cardassia, and to be willing to allow its citizens to join the Federation and even apply to Starfleet. The Detapa Council also favors withdrawal from Bajor, but stalls on the question of reparations, which angers the Bajoran population and leads to a provisional government that's in the control of more radical elements.
• These elements, although officially neutral toward the Federation, start a program that effectively combines some of the features of the more vicious elements of the Ferengi with those of the Orion Syndicate, and specializes in stealing about as much as they can from the Federation and Starfleet. They also end up attracting people from the Federation who are disillusioned with it, for one reason or another, including Thomas Riker, who helps them make off with a mothballed prototype ship that Starfleet had never gotten to work properly.
• He's aided in his hijacking by an embittered former Starfleet commander who had never worked through his grief and anger after losing his wife at Wolf 359, both because he never had the chance to confront the captain-turned-drone that led the Borg cube, and also because he'd never been posted to the former Cardassian ore-processing station which in turn would have led him to a personal epiphany.

So... I guess it could work.