FireFox can support Ajax, and FireFox can run on Linux, so yes if they use FireFox or any other up-to-date browser. It doesn't matter what platform they're on, just their browser.
Ajax stands for Asynchronous Javascript and XHTML. If your web browser supports Javascript and XHTML, it supports ajax.
Firefox, IE, Opera, Safari, etc, all support ajax, regardless of platform.
yap me too, when i was programming a page using javascript, it work on my opera, after finished one of my user using IE, and all thinks blowed up my head.. ouwch...