Yes it is... Look at ulis game.
How ... well thats up to you really. If you learn c-script then it will be fairly easy to realize how. I made a mario clone awhile back if I can find it ill post it here maybe it will give you an idea of where to begin... Mind you I never completed it and theres still a ton of bugs. I can tell you that I got my movement code from grimbers fps tutorial with a few minor changes it was easily adapted.
Ok found it. Just press ok to the missing wad... it should run fine with out it. I dont think I used anything thats not in the standard wad so you could just possibly replace it with that. I just had added a few extra textures to the standard wad and saved it as a new name.
As I said theres still alot of bugs esspeically in the jumping. Youll get stuck mid air and hover over blocks... There were a few post on how I could fix this just never did them as it wasnt a serious project anyways... More of a learning expeirence.
Mind you this was done all in one day so I really dont think its too bad concidering that. It might at least give you a starting point.
Heres the link...
Pisquali Bros... A crappy mario clone.