In one sense, and AFAIK only one, it does. He counts as a Republican for purposes of determining who's the majority party (course if it ends up so wobbly one member makes he difference, I'm sure he pulls a Jeffords), and the majority party selects committee chairs and gets majority representation in committees. So he's truly a "Republican In Name Only" and yet that actually matters!
If his is the vote that determines which party holds the majority, do you think he'll allow Republicans to fill the chairs, or will he insist that they be filled with RINOs?