As the Borg are far more advanced than the Cybermen I think they would willingly join the Borg collective. They would see it as an advantage to be part of a bigger and better "collective."
If the Cybermen are anything they are practical.
The Borg would be pleased to gain the drones with no fuss no muss (finally volunteers!)
FYI: The Borg were loosely based on the Cybermen. During the first episode in which the Borg were introduced the names of all the actors (to date) who had portrayed Doctor Who were listed on one of the bridge consoles of the Enterprise. It cannot be seen in the film but the crew did that as a "nod" to the inspiration of the BBC series.
