Seven : "The optical assembly is properly aligned. I am ready to access the main power supply."
Kim : "After you."
(The pair climb down, and Seven begins to reach into a conduit)
Kim : "Wait! What are you doing, there are five million gigawatts running through there!"
Seven : "The exoskeleton on this limb can withstand it."
So if the drones bodys are even build to withstand this force, I would guess their shilds would not overload.
(Why some phaser guns work is something compleatly different.)
Of course that assumes Vader does not forsee it, a very unlikely possibility for someone so powerful in the dark side of the force. The Borg Queen consists of extensive amounts of non-living matter, she will extremely vulenrable to Darth Vader.
No, she would not. You can't kill her. Picarad killed her "body", does not mean she is dead.
This whole scenario may come down to how quickly Vader can find and control the queen...This would make a neat short story....
He would need to control the hole collective. Trillion of minds more years of knowledge every living beeing could hope to have. Not a save place to go.
And he would be a worthy target of assimilation. Considering that vader is driven by anger and self hate. He fell for palpetine who could not even offer him, what he was searching for. The borg could have and I guess they still can.
So sending vader to the borg would be quite conterproductive. Vader is a broken and very tragic character. To send him to a place, where he might find a new start/oblivion would be tempting. As a jedi he might have fought the temptation, as a sith there is just no reason.
To rule the galaxie as king and not as the side kick of his former master. Immortal. And maybe even the possibility to see his lost love again.
So after consideration I guess he would join the borg. They offer everything he was searching for. They are the order and the honesty he graved so deaply. (Even more after beeing betrayed several times)
She'd still have to be on that cube, instead of her ship or the Unicomplex.
The borg queen is everywhere and nowhere at the same time. She is the voice of the collective.