There is a new paper (pdf) from Harvard, by Andreas Madestam, Daniel Shoag, Stan Veuger, and David Yanagizawa-Drott, and it seems the answer is yes, the Tea Party has been effective in electoral terms:
This paper examines the impact of political protests on citizens’ political behavior and policy. We study the effect of the Tea Party movement protests in the United States on voting in elections and on legislation by representatives. To identify the causal effect of protests, we use an instrumental variables approach that exploits variation in weather on the rally day. We find that the protests increase turnout in favor of the Republicans in congressional elections, and decreases the likelihood that incumbent Democratic representatives run for reelection. Incumbent policymaking is also affected: representatives respond to large protests in their district by voting more conservatively in Congress. In addition, we provide evidence that these effects are driven by a persistent increase in the movement’s strength. Protests lead to subsequent protests, as well as an increase in membership, monetary contributions, and media coverage. Finally, the estimates imply significant multiplier effects: for every protester Republican votes increase by at least eight votes. Together our results show that political protests can build political movements that ultimately affect policy.
How this translates into policy outcomes, of course, is another story. And this is effectiveness at a very micro level. It is entirely possible to believe these results about local mobilization, and think that the Tea Party overall makes Republicans less electable or less effective once in office.
Addendum: A revised and improved version of the paper is here.