Probably not:
Given his [current RNC chair Priebus] performance and given the popular opinion that it is the social conservatism of the GOP that is having the greatest impact on its perception as a national party, it would only make sense that a libertarian Republican would be in a good position to challenge for national leadership. But just as we saw with libertarians Ron Paul and Gary Johnson, when given the choice between a libertarian Republican or an establishment or socially conservative Republican, the Republican electorate will always choose the latter.