I think that you have to take into account, at least slightly, the evolution of Q as a character. Initially, he was the all-powered Watcher character which often sounds a death knell in series (Odyssey 5)- although the rare one (like Star Trek, Fringe, and partially sorta-subverted in Highlander) which integrates the character and explores their back stories and such will often succeed.
Roddenbury decided to make yet another campy villain, this time with the powers of a god. After Roddenbury passed away, however, it allowed them to play with the idea that maybe he wasn't a villain after all. What if he was a good guy (or maybe simply grew up into one) who was trying to help, using somewhat questionable methods and an abrasive personality? By that point in Voyager, this was very firmly in place. I don't think that this is a case like What If The Doctor Was Turned Into A Dalek (the closest similar premise I can think of) as much as Q trying to get his kid to stop screwing with the lesser beings.
Further (and my memory on this could be off) Q was assigned by the Q Continuum to watch over his kid to prevent him from growing into a menace. One could certainly argue that screwing with the Borg is pretty much a perfect example of that. From the Wikipedia page on Q: "Q asks Janeway to mentor his son, and the two adults agree that the boy will remain on Voyager, without his powers, and either learn how to be a responsible, productive inhabitant of the cosmos, or spend eternity as an amoeba. Eventually the young Q comes around, but the Continuum is not entirely convinced, so in negotiation with Q, they come to an agreement. Q must eternally guard, observe, and accompany the boy to ensure his proper behavior."
One could argue that Q knew that this would happen, and tried to protect Little Q from being in trouble, or alternately that he knew Little Q's powers would be removed which WOULD make him susceptible to Borg assimilation. That, then, calls up a slightly different question: do the memories and knowledge of the individual become spread into the collective? We know it happened with Locutus (or kinda-sorta) but he was a special case which was planned ahead of time. For the typical capture and assimilate though, it may not be the case. The knowledge of a Q given to the Borg would be devastating. However, ultimately, I don't see how Q himself would ever allow that to happen to his son, so it's all likely a moot point.