TL;DR short answer: Yes it's possible, but it's a pain in the ass and only kinda half works the way you'd probably want.
Long answer:
Assuming OP was asking about Fallout 1 only and specifically, the only way to do this is:
Replace all the graphics files for the main character with files from a different character/type, by manually copying and renaming all of them (batch renamer program helps here).
Or, going into the exe and modifying the pointer(s) that point to the (fe)male PC's default appearance. This changes when armor is equipped, so it's only useful if you're playing without armor. As .Pixote. said though, you could use the graphics from F2RP, but unfortunately I'm not aware of a way to replace the graphics files for when armor is equipped, without that also changing the appearance of all non-PC critters who wear that type of armor.
As far as I'm aware, the sfall/timeslip functions mentioned above DO NOT work for Fallout 1.