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Well that's entirely dependent on whether the Borg completely negate the death star weapons.
You only get a couple shots on any given frequency modulation of your energy weapons.
So as long as they have like.... 6 or 7 ships? They're good to go. After losing two or three ships. Just keep shooting until the death star goes boom.
If they hide inside a cargo ship and get tractor beamed into one of the bays, then I'd say it's only a matter of time before they control the entire death star.
It also depends on whether the Borg consider the death star a threat or worthy of assimilation. Given the accuracy of shooting of those on board, I highly suspect the ship's technology would be assimilated and then its inhabitants converted to drones.
Guys, the dog just shot itself.
The whole thing about being able to resist energy weapons is silly though, and the logic doesn't exrrapolate well at all when you have a laser the size of a small moon blasting at you. The Borg's only chance is to swarm the death star with too many ships too quickly and stay below its effective range.
The planet killer can't fire very frequently. Realistically, they just need to get within transporter range, send drones over, and start assimilating the ship. If they can avoid the first shot from the superlaser or just have a second ship, they're probably fine. Unless the Death Star has Vader on board.
The Force is irrelevant. Vader will be assimilated.