I got ya... but there's no way to do it 
The RESTHandler that handles our request when we execute a client call to a web service method we've tagged as a ScriptMethod is synchronous. It implements IHttpHandler, not IHttpAsyncHandler.
I've gotten different responses from MSFT regarding why this is the case, but it seems that the consensus was that since the next version of ASP.NET AJAX supports calling WCF methods and those don't have to use ASP.NET threads anyways (they can live at an arbitrary endpoint not on the ASP.NET stack), then there wasn't a need to implement the RESTHandler using IHttpAsyncHandler because it would scale without moving the work to a background thread ... Now, my response to MSFT was, "wasn't WCF out before ASP.NET AJAX 1.0 dropped? (Yes.) Then why wasn't WCF supported to begin with?" Still waiting on an answer for that ... but most likely it'll be the so many features, so little time answer, which as a developer in the corporate world, I understand, even if I think this was a big missing feature.
So to answer your question, no, there is no direct exposure to the BeginWebMethodName, EndWebMethodName that you're asking about.