If I'm not mistaken, doesn't offline mode on one computer de-authorize the others ability to do the same? Steam won't let you log in to two different computers, so having Offline Mode on a number of computers would be a pretty big loophole in the otherwise lenient DRM. I'm checking the steam documentation and I'm not finding a lot of details on the particulars.

On a separate note, if you're playing FO3, you should be playing it through FOMM (Fallout Mod Manager) to make use of all the juicy mods (better textures, more armor/clothing, better companions, etc).