I have signed up(paid) for Google site search. They have me a url of a sort of web service where I can send a query to it, it searches my site, and it returns XML of the sea
You can't load external files with AJAX. However, you can set up a file on your own server that makes the content available on your server. For instance in PHP, you could write a file googlexml.php:
And then you could access that with AJAX. I'm not sure if Google's terms of use will let you do that, but if they do, then this is an option.