Agreed completely. The conference doesn't help, but it only doesn't help because the program is making itself irrelevant all on its own.
If you're an elite program, nationally relevant, it doesn't matter how crappy your conference is. You'll get big-time recruits and positive press. See Gonzaga.
The only way conference affiliation can help you is if you're a bad program trying to sell recruits on competing against the best (e.g. the very early Calhoun years). What keeps UK, Kansas, Duke, UNC at the top isn't that they play in P5 conferences, it's that they're consistently good-to-dominant all year, each and every year.
The conference is just an excuse. If we're performing to the expectations of this program, what conference we're in matters zero.