If you turn Javascript off, the only information the website can get is user agent and IP, which would narrow it down much less than using Javascript even just among the pool of non-javascript users.
Keep in mind that there are a lot of services that load sites without Javascript enabled (scrapers, mail, preloading).
Pretty sure you can get some extra information through CSS media queries that only trigger a server hit when active (allowing you to add, say, screen size and color range to the fingerprint even without javascript).
Keep in mind that there are a lot of services that load sites without Javascript enabled (scrapers, mail, preloading).