Yes, modern browser (IE6+, Firefox 2+ and Safari 3+) with JavaScript enabled is a requirement for full functionality. Although some core features work without JavaScript, many do not - multiple file uploads, request that tries to modify or delete data on the server (try moving anything to Trash or completing a task) etc.
I was under the impression that all core features worked (with simpler functionality) without JavaScript. Not any more?
If JavaScript *was* a requirement, I'd expect a lot more use of AJAS / AJAX...