As far as I know, it's possible for a client to block JavaScript in his browser. If that happens, what will happen to AJAX calls? Will they work or not?
AJAX is JavaScript. No JavaScript, no AJAX.
No, the J in AJAX stands for JavaScript - if Javascript doesn't work, then neither will AJAX.
The AJAX call will not be executed if the user has disabled JavaScript.
If javascript is disabled it will not work... You should read into Progressive Enhancement and "HIJAX"
I never bother with users without javascript, well I do bother but only to a certain extend. It might be a bit harsh but people or companies which disable javascript know that they will be missing out. Ofcourse text-only browsers should not be forgotten.