Is it possible to generate bitcoins with a Google Chrome extension?
Well, I cannot speak for that specific generator. However there has been a javascript generator already in use and Chrome extentions are I believe javascript based, so it is very possible.

The javascript generator only uses CPU mind you, and is quite slow.

As for using the GPU, that is a possibility with some of the browser plugins out there, such as Unity. However a native browser? not very likely, they try very hard to restrict hardware access.