Playing devil's advocate: Let's assume a Borg nanite could assimilate a Q while it/they assumed a corporeal form. Depending on it's collective/queen's objectives, it could wreak plenty of havoc across known time and space. But we're dealing with the Q here, so at any point they could "assume control" switching from chaotic good/neutral/evil as they see fit. After allowing the collective to have it's fun, with a snap, we're back to square one. In the event of actual assimilation, let's just assume the known universe is kaput. Take your pick.
Another option: Assimilating a Q assuming human form is the exact same thing as assimilating any other human. They get no more knowledge of their powers, and maybe only some understanding of the universe as a whole because they only get what's able to actually work inside that meat brain, and not the whole sum of the being of the Q who was assimilated. The nanites only function with the physical aspects, but none of the metaphysical, in this case.
Put into that frame, it's like Marty McFly using Gray's Almanac to place bets. A temporary boon with limited implications compared to the span of the Q continuum.
they only get what's able to actually work inside that meat brain, and not the whole sum of the being of the Q who was assimilated.
This seems logical, but when the continuum revokes or disables Q's powers in TNG he still appears to be a super-intelligence. I would think even that degree of power could potentially augment and improve the capabilities of the Borg by orders of magnitude.
I don't know if he appears more intelligent than an average human. He tells the captain to change the universal constant of gravity, because that's something he used to be able to do, and when reminded that he can't he has no helpful suggestions.
Q would have to allow the Borg to assimilate Q's human form though. I say this because Q should already know everything about the past, present and future. It feels like we might be getting into paradox territory now...