Quinn is literally in the room when you're given instructions to go to Hoth and redirect Armaggeddon Battallion back to Corellia, where they're supposed to be. He can be with you when the general in command confirms that they were stationed there on Baras's direct orders, when you can either convince him to disobey those orders ("Imperials are dying whilst you sit on your hands") or execute him because murderloldarkside.
It just feels a little like the consequence of moral expectation railroading. As in, assuming everyone who plays is going to be super dark side about it and kill everyone in their way. And, hey, if that's the case, then sure. What motive does Quinn have to side with them? Baras might be objectionable, but the warrior's hardly any better in that regard. But if you don't, if your warrior is more patient and consciencous of the bigger picture as the story very much lets you be, Quinn's actions are a little bizarre.
You are bringing up short term problems, sure if you look at Armageddon Battalion being on Hoth, it's a short term bad thing for the Empire in that battle. However even with Armageddon Bat showing up on Corelia the Empire loses, so in the long run it would have been better for the empire to have lost Corelia and still had Armageddon Battalion around then to have wasted them on a mission that was never going to win.
As far as I can tell the invasion of Corelia wasn't the choice of the Empire as a whole, but the actions of one Darth that caused a huge amount of losses for the Empire and failed to achieve it's over all goal.