At this time ok it is working straight I only used one search term and the results I get are all pointing to The WordPress site.
But IMHO you are taking a great risk.
Google is more and more taking over as far as I am concerned even hijacking websites.
I think you should be very carefull with Google.
Offcourse it is a great search engine, but the problem with Google is sometimes they give really unrelated search results.
I think for the best it is still a good choice to keep also the search engine from within WordPress as a choice for users from this excelent and simple website.
Untill now all results I got before you changed it to Google where very satisfying.
So maybe its a good idea to keep a sharp eye on this new change.