The context from which my question has arisen is this user script which locally removes ads from Ixquick.com, which is an anonymizing 'proxy' search engine that gives the results from Google's index while not giving any info of yours to Google at the same time.
But the script makes use of Google Hosted Libraries, with this line in the userscript code:
// @require http://ajax.googleapis.com/ajax/libs/jquery/1.6.3/jquery.min.js
Is this Google JS file, able to store or process, on Google servers, the URL of the page I'm on, ALL the content on the page (which reveals the search information I entered into Ixquick), my IP address (which reveals ME - and could it also cut through TOR's IP address obfuscation and somehow reveal my exposed IP, as well?), or even other things such as passing on my browser user agent, all to Google, thus defeating the point of using Ixquick in the first place?
Again, this is not about what Google's JS files necessarily do right now, but what the architecture is capable of, and thus what it could dynamically be updated to be able to do without our control.