If we go with the original trilogy, perhaps the force can’t be tapped into by unfeeling automatons. However, the prequels made the force biological. The Borg keep the biological abilities of anything they assimilate. And the assimilation means they will gain the knowledge of how to use them. The only way they wouldn’t keep it is if the assimilation nanoprobes somehow destroyed the midichlorians. We are shown that having emotions period is a liability to the Jedi, and since they are Force users, that means emotions are not necessary to use the Force.
In fact, since the nanoprobes actually contains small replicators, it wouldn’t be too hard for the Borg to give every drone Force powers. Perhaps the former Jedi would have to make it back to a testing facility, but, then again, that’s required for full assimilation, anyways. The only hope of the Jedi is to kill their own if they are assimilated.
In fact, I only see a Jedi victory if they get smart enough to steal the Storm Trooper armor for use in all battles, rather than fighting without any protection but their own ability to use the Force. Eventually one person will slip up. Force suggestion is great, but it’s nowhere near the first technique the Jedi will try. And I do believe the Borg will eventually adapt: all you need is a stronger signal from the queen (once she’s formed) to override the suggestion.
So I see a Jedi victory as follows: The Borg attack a planet in the Republic that doesn’t have much defenses, and take it. They beam down to gather information by assimilation. Now knowing about the Republic, they realize that, while the bigger ships are great, the big prize are these warriors with powers they don’t have (and perhaps the outrageously strong lightsabers that the warriors use.) Arrogant as always, they simply confront the Jedi head on, beaming down to the Counsil, after the Jedi numbers have picked back up to prequel levels, and all are present. The Jedi fight well, and the Borg are nearly overwhelmed, but one Jedi lets his guard down, and gets stabbed. Luckily (or due to the Force), the Jedi had just heard about assimilation, and, not taking any chances, attack the assimilated Jedi. Unfortunately, he’s a pretty good match. Fortunately, one of the Jedi gets the idea to reach at his mind, and realizes that he is very suggestible, and has him kill himself. Knowing this, the Jedi use Force suggestion to have the Borg drones fight and kill themselves, while the Jedi slowly leave.
Not knowing what to do with this new challenge, the Borg activate the Queen. She reviews the broadcast memories of the fallen drones, and realizes that the drones were controlled. She also knows about the midichlorians, but does not have enough information to replicate them. So she knows she’s going to have to get involved herself, along with newly engineered stronger willed drones.
Fortunately for the Jedi, the Borg are still arrogant, and still send a cube, giving the Jedi enough time to prepare. Every Jedi dons Storm Trooper armor that the Republic was going to use for their new infantry soldiers. Fortunately, these are all now Force users and thus Jedi (otherwise why wouldn’t they help) due to blood infusion. Unable to use Jedi mind tricks, they fight by themselves. The queen, of course, stays out of the way of battle, but at least some Jedi are pilots and attack the cube. Fortunately, the Borg did not get too much information about ships in their first assimilation, and so Death Star level ships are enough to blow the cube out of the sky, killing the queen.
Of course, the Borg themselves are fine, but, after two losses, they do what they did with humanity and decide to lay back for a while, studying the new Republic from afar. Sure, there are a few more skirmishes, but these are largely space-based, and, seeing as the Borg aren’t that great against even vastly lower powered ships, the Borg don’t do that well. Eventually they decide to just sit back and let the Republic deal with threats from other sources, hoping to pick them off after they lose to another Empire.