As Ashfaq Mohammed linked, I agree with Miguel Angel Baeyens and I don't believe that's possible,
Ajax and the IE-Plugin are two different clients when accessing a QlikView applicaiton that you can choose when opening a Qlik document.
Both clients don't behaviour the same, don't communicate the same with the server, don't use the same port, don' use the same technology and are not executed in the same place...
The challenge and the reason why I think it's not possible is that when you have requested to open an application with the AJAX cliente, a communication is stablished throught port 80 and basically you're using a client that executes on the server but when you open an application with the IE-Plugin you're starting a communication with a different port (4747 if I recall) and the client is actually working inside the browser (on your machine).
That button would need to:
a) Close your session with the actual client
b) Retain somehow the document state (at least the document name and all the selections made)
c) Start a new client without closing the session and apply all the values already selected
It seems very complicated and right now I can't think in a direct application for that button
Still, a very interesting idea.