Possible duplicate of:
should-i-link-to-google-apis-cloud-for-js-libraries
also many other discussions, including:
Where do you incl
I believe that the Google JSAPI is also asynchronous and helps avoid the "toll booth" best described by "Imagine there's a 4-lane highway between your web browser and the internet itself. This highway is optimize to let pictures, text, and css fly by. But, when it comes to external scripts, the highway creates a toll booth that slows traffic. The worst part is that pictures text, and css caught behind these scripts have to wait until they pass through" - Andres Vidal
The toll-booth is critical and must be avoided at all times.
I think this method will help you a lot for the following reasons:
Google uses a Content Delivery Network and that will make that the users that are far away from your location can download your jquery libraries faster than if they did that from your site.
Also it will reduces the request to your server and will make first time users to download jquery javascript from google's server, and if the user has been in another similar site with this kind of implementation he won't need to download it again.
So I think that this will help you app/site