i would agree with woods the only possible way i can think of is running the online parraelle app that allows you to run a widows os through your browser then then load up Firefox, but at that point why run firefox, the search engine is optimized to run onto google. and firefox isnt a search engine, to run a different search engine just type it into the browser.
Ben, The Chromebook can run software. I have two native (i.e. non-web-based) applications running on my Chromebook: Scratchpad and SourceKit. However, I don't see Firefox running on a Chromebook any time soon, if ever.
No to Firefox, obviously. It's a browser. You can use other search engines, though. Chrome lets you set a default to Google, Bing or Yahoo! for "monobar" searches. And you can always bookmark any others you'd like. You can set that in preferences.