I'm not sure this would even be possible within the existing canon because the continuum could revoke the powers of the Q who was being assimilated.

Excluding this canonical failsafe, I think it would most likely mean that the Borg would be able to eventually replicate the powers of the Q within the collective. This posses another interesting question or thought experiment.

Would the Borg even be driven to assimilate any more worlds or beings at that point given the fact that their entire motivation is understood to be the pursuit of all knowledge in the universe? The Q seem to be near omnipotent and omnipresent. So, in theory, if the Borg gained access to this power then it seems logical that they would no longer be driven by the same motivations, and would even cease to be Borg at all since they would necessarily reclaim a sense of individualism.

Either way, great question. This is why I love Lemmy. The Trek community here is amazing.