I think it is convenient for the left to view the Tea Party as a GOP creation. Which I don't think it is. It is also convenient for the GOP to view it that way, as they try to coat-tail to the extent the Tea Party gets traction.
It is undeniable, though, that the average tea party person is more likely to share GOP views than Dem views, although I know a few Dems who are part of the tea party locally.
If McCain had one, who knows what would have happened with the tea party. On the one hand, McCain and even Bush are not people who govern in the ways the tea partiers profess to want, so you could still see the movement come about. But on the other hand, it takes a certain amount of 'critical mass' to get people motivated and to turn out for something like the tea party events, particularly those members who haven't been politically active before. Even if those same people didn't like McCain, there may not have been enough dislike or concern for people to show up to tea party events.
You're right that the GOP had absolutely nothing, zero, zip nada to do with the organization and creation of the Tea Parties. In fact many GOP leaders initially turned up their noses in disdain and criticized the Tea Partiers. At least they did until they realized how popular the Tea Parties were becoming among much of their base and they they were scrambling like mad to get on board. Hypocrisy is not limited to the Democrats for sure.
I would guess maybe the largest group among our local Tea Party rallies has been registered Republicans, but I think they were only a plurality and not a majority. The Independents and Democrats and others together most likely made up the majority. We were not in any way interested in party affiliations or anything else among those who participated. We wanted people there who shared the primary Tea Party goals of smaller, more effective limited federal government, less oppressive taxes, and appreciation for the intent of the Constitution.