Oh, this idea is bad on so many levels.
First, they're not going to get big name celebrities. For many reasons, number 1 being, the agents/managers of said celebrities would never agree to it. Secondly, these celebrities are just not going to be willing to do what it takes to run the race. Sarah Jessica Parker is not flying coach for a month. Neil Patrick Harris is not taking 24 hour bus/train rides etc. So, at best you would end up with a cast of "C' & "D" list people (Bachelor show rejects, 1 hit wonders from 20 years ago, etc)
Even these people, though, would attract attention while traveling (especially while traveling with a film crew) and lately it seems that TPTB are doing their damnest to keep spoilers at a minimum (not that they can thwart the super geniuses of RFF)
And lastly, but IMO, most importantly, I hope the braintrusts behind this idea remember the basic premise of this show: Ordinary people doing extraordinary things!