Rice is probably a school that could pull independence off. The question is would all of the schools they'd want to play be willing to make space in the schedule for them? Schools only have 3-4 games to work with OOC and one is usually an FCS teams and for the G5s oftentimes there's one is not two buy games against the P5. Some schools also have some established OOC rivalries you'd need to work around:

UTEP vs NMSU
SMU vs TCU
SMU vs UNT
UTSA vs Texas St (hopefully becomes more permanent)

Heck, Rice is even struggling getting crosstown rival Houston on the schedule.

Rice is a school full of a lot of smart folks and I think they will take things cautious and stay in C-USA for the stability. They may loath the newcomers but it's 3 guaranteed games against Texas schools a year. They have one of the tiniest alumni bases in FBS so it's not like they bring a lot of television appeal that they could market on their own. As an Indy they'd probably be playing on the LHN for about $27.94 a game.

It's an intriguing idea but I don't see it coming to be.