1. CMU is the top CS school nationally; the basic quality of the education makes up for the lack of previous experience
2. CMU crafted a program specifically for students without previous experience to counter this effect; most schools do not
I think most people would say yes except to play devil's advocate. Becoming a top caliber athlete requires years of conditioning, experience predicting trajectories of fast moving targets, ability to read your competitors, mental fortitude, flexiblity, and more. Why would we expect a field that prides itself with top caliber professionals in a competitive environment to be any different?
To my mind, the fields which are known for requiring training from childhood are sports and the performing arts (music, theatre).
And if I had to guess, I'd speculate this is less because it's intensely difficult to play sports or learn to play music, but because so few people can become professionally successful in these fields (there's only room for so many sports/music/film stars). CS doesn't have this problem (the demand for programmers is skyrocketing), so we shouldn't expect folks who learned to program in childhood to have any more than a mild-to-modest advantage.
What early education provides is a safety net when things become tough. My classmates without this preparation had a much more difficult path and many eventually dropped out. The psychological effect of impostor syndrome is a component to picking field to study in college; those who feel they have a harder time than their peers are less likely to continue in the field long term.
I've heard that idea in a lot of places, but it's never matched up with my personal experiences. I did my undergraduate at CMU, and plenty of the better programmers there I knew hadn't done any programming before they came to CMU.
But of course, this too is anecdata.