The ratings services will insist that it doesn't, but it certainly does. As a member of the Pac12, an offer from Utah now influences the rating of a recruit much more than it used to.
As for BYU's ranking, I don't buy that either. They're getting the same Mormon kids they've always gotten, and they still win most head-to-head battles with the U, just as before. I don't think it'd change much in a P5 conference, either. As they say, "It is what it is." At least when BYU recruiting is the topic.