When I (and many others) discuss strategic voting, we're primarily talking about players who deliberately withhold votes from the first place team (but still vote legitimately among all remaining teams). I don't think that full blown strategic optimization is likely, but I am willing to believe that some players would deliberately avoid voting for their most direct competitors. It's a minor form of strategic voting, but it's one that can have a large impact.
To be perfectly honest, I don't think this sort of voting affected this Brawl much, if at all - most if not all of the votes my team lost after being in the lead I can understand after looking at the submissions. I think a couple of our submissions were better than they finished, but I also think that's some combination of bias based on liking "what belongs to my team" and a difference in taste with other members leading to a submission I liked less finishing high.
That said, the possibility of strategic voting and the bad feelings associated with it certainly made our team rather unhappy during the Brawl. I'm trying to come up with suggestions that would reduce the appearance of strategic voting, even if it's impossible to eliminate or prevent it altogether. Under my anonymous submissions model in the later rounds, it would be much harder for accusations of strategic voting to have any merit, whatever mathematical possibilities of strategic voting might still exist.