No, it doesn't. Picking between microstates isn't a "modification" of the universe, it's simply talking about the observed probability of something that already happens all the time.

Although now that I think about it, this argument should apply to more traditional anthropics as well, if a simplicity prior is used. And since I've done this experiment a few times now, I can say with high confidence that a strong simplicity prior is incorrect when flipping coins (especially when anthropically flipping coins [which means I did it myself]), and a maximum entropy prior is very close to correct.