Luckily, the Evernote Web Clipper has a feature that seems to solves the issue above allowing you to simultaneously search on Google and also on your Evernote notes.
To enable that capability all you have to do is to right-click in the Web Clipper and then make sure you have the Related Results checkbox enabled. I believe this is available only in Google Chrome and Apple Safari for now.
|Evernote Web Clipper Related Results to add simultaneous search capabilities with Google|
On your next Google search, you should be able to see results similar to the following picture (with the Evernote results boxed in to the right).