Of course. We used to carry around about 4 or 5 floppy disks in Uni at the time. Started with the shareware version which had the first episode free, then *ahem* your friend had the fully registered version (think you couldn't actually buy the game in the shops) and all 3 episodes were open. Was amazing on Uni network with coop play. Totally had to beat it to finish degree...
Oh, and think was the only version where you could link up 3 network machines to have 3 monitors (front and sides). Was well cool. Think was dropped after shareware version. Also look up RandDoom (or RndDoom) where is randomizes where the monsters and keys are. Totally made it a new game.
There was also an OpenGL patch (DoomGL or GLDoom?) to make the original's graphics better.
Ah, those were the days
Cheers