How to launch a Game client such as League of Legends?

I was wondering if it is possible to do the following.
Launch League of Legends [Or any other game that runs through it's own program] through a browser [Not in the browser but connecting through the browser to send/receive signals through that connection] while keeping it in a client-based mode?

I.E. Everything sent or received from the server goes through say... Google Chrome then localizes to my PC through the game client itself?