No, I can't imagine. For example, the United States has fixed election dates and their voting turnout records are fairly low, but there are a whole bunch of reasons for that. Frankly, I think if they didn't have fixed election dates in the U.S., they'd have at least as low, if not lower, turnout. Note that American turnout rates are now the same as Canadian, at least in the last presidential and federal election. Even there, the American case doesn't work. And you can never generalized from single cases.
So no, there is no data to prove that.