Short answer: Fallout 1: Yes. Fallout 2: No, not without a MOD.
Long answer: In order to turn into a supermutant, you need to be exposed to the FEV. The only place you can expose yourself to the FEV is at the Sierra Army Depot and the Oil Rig. Both places have the "modified" FEV that kills you. The Elder will describe how you can look forward to dying. The "original" strain of FEV can only be found in F01. You can turn into a Super Mutie in that game , and kill the Overseer :7
Now, someone might come out with a MOD that lets you "look" like a supermutant. I know there's one that turns you into a fire gecko, complete with fire gecko breath.