Yes he would. He does this kind of stuff all the time. He was one of the first and only Republican Senators to call for Clinton's resignation. Many GOP Senators may have had the same idea, but they weren't dumb enough to state it before they gauged the sentiment of the country.
It looks like he will be the incoming Senate Majority Leader.
If he was going to be Majority Leader, it would have happened by now. This little stunt kills it for him.