I'm saying neither.
1) I've found no polls to suggest that Joe Public, to generalize, knows what a "Libertarian Party" is.
2) Ron Paul needs the infrastructure of the mammoth GOP to get elected, just as most candidates need the support of one of the two major parties. It cuts both ways and sideways. Republicans need the GOP to get elected, and Demos need the Democrat Party to get elected. They need them so much, that conservatives will run as Democrats (Sam Nunn), and liberals will run as Republicans (NYC's Guliani, and Bloomberg. NYState's Pataki, not to mention Senators from Ohio and Maine, et al).
The polls I've seen show that an R or a D after the canditate's name carries a great, and disproportionate weight with voters, even when the candidate's views are 180 degrees out of phase with the voter.
Ron Paul might be able to get re-elected as a Libertarian, but then the GOP, seeing that they have no dog in the fight, would find a dog to put in the fight. Whether Ron Paul would survive this hypothetical (since you've suggested this hypothetical) is anyone's guess, and would be something that local Texas political scientists would be very interested in, for about six months, tops.
Rick