A seven-game playoff series is not significantly fairer than a five-game series when home-field advantage is considered, according to Brian Dean's paper in the arXiv, which I found while googling for something only tangentially related. ("Fairness" is defined as the probability of the team with home-field advantage winning the series.) It's not significantly fairer when home-field advantage isn't considered, either.
It is a little bit fairer, though (i. e. the better team is more likely to win in the longer series), as I wrote about back in June.
In case you read it: the cases the paper mentions where the seven-game series is "less fair" than the five-game series (i. e. the better team is less likely to win) are certain cases in which the team with home-field advantage is actually significantly worse than the team without it, even when playing at the first team's home. This doesn't happen for matchups that exist in practice in the playoffs, I don't think; for one thing, the team with the better record has home-field advantage in most such playoff series.
Also, the final section of the paper addresses the question of "morale"; if a team wins a game, are they more likely to win the next game? (Or less likely, because they start slacking off?) And how does this affect the probabilities? From what I remember, this sort of behavior doesn't show up in the regular season -- teams are as likely to win tomorrow if they win today as if they lose today -- but it might show up in the playoffs, although the sample sizes on playoff series are too small to say much with any confidence. But my guess is that pitching rotations are more important than morale.