Yes it’s possible, but only for Fallout 1 when installed as a DOS32 application (but Fallout 2 is Win32 only). I haven’t actually played the game yet, but I plan to. For some reason, I have not been able to get Fallout 1 or 2 to run under Wine 0.9.17 in Fedora Core 5 (fc5) but I’m sure there’s technowizardry out there to accomplish it. However, I’m still a Wine n00b. On the plus side, click on the blog title for a great link to a how-to on linux gaming written by a young guy named Firewing1 who really knows his linux stuff.
Edit: clarification and typos