Consider this: An instance occurs where two Borg Collectives are formed. I'm not asking how that would happen, I'm asking WHAT would happen. The two groups are the same in practically every way, but they were somehow programmed to be enemies. Would one eventually assimilate the other, and become one? Would they simply fight until there's nothing left? Thank you for your time.
We see this happen in the episode VOY: Unity. A small number of Borg are disconnected from the collective and eventually (after 42 minutes, coincidentally) manage to reconfigure theirselves to form a non-Borg "co-operative".
Their immediate fear is that the presence of a Borg cube will attract the attention of the Borg Collective and, given their known predilection for attempting to assimilate anything that is novel or useful, I think we can be pretty certain that they would attack if they knew about them.
So the answer to your question is a solid yes. If the Borg Collective encountered another non-Borg Borg Collective, they would likely make stern efforts to assimilate each other.