I just went back and tried myself. I've been playing FO2 lately, so I had forgotten my issues with FO1. I had a similar issue.
When in fullscreen, I can ALT+TAB and run programs outside the game, BUT if I return to FO1, the screen is black and is revealed by moving the mouse cursor around
When in windowed, I can ALT+TAB, but the screen is pretty much fubar.
I don't know why you're having trouble being able to ALT+TAB, but it may just be beyond the game's ability to allow it. FO2 is much less finicky. Sorry I couldn't help. I'm going to try a newer version of Sfall and see if anything changes.