While the Libertarian Party never seems to get more than a few percent in national elections, small 'l' libertarians are not insignificant. The GOP won't do well without most of them, IMHO. In an exit poll last November there were only 32 % conservative. The remainder was 47 % moderate and 21 % liberal.
I know of nothing that confirms that Libertarians support the Republican party. I assume the majority support the Libertarian party. Most Libertarians I know tell me there is no difference between Democrats and Republicans. While I would like to agree with your reasoning I don’t think it holds water.