I don't know about IE 2, but Netscape 2 is still sort of usable. I've been running it on my PowerBook 180c for a few days, and as long as you have the exact version of Netscape 2.02 that allows you to disable Javascript, it is really quite usable, if a bit slow and butt ugly (due to its lack of CSS support). But for the most part, everything works, such as the HTML version of Gmail, and this forum.
For a while I was actually going to use NCSA Mosaic, but I've since discovered that like you said about IE 2, it doesn't really work. I couldn't even get Google to load under Mosaic - it got stuck in a loop redirecting between Google.com and Google.com.au.