Eh, that the Frankenstein monster was 'created' only represents a facet of what made it such an effective antagonist, IMO. It seems the particular facet of 'created in a lab' isn't too transferable with the playable PC races, but if you identify some other facets such as 'tabula rasa', 'abandonment', and 'eternal isolation', I think it's entirely possible to capture the essence of the Frankenstein monster in a character. Were I to do this, I'd likely start with a background concept along the lines of: Sewer Caliban is captured in Port-a-Lucine and brought to a scientist in Lamordia for experimentation. Already thought of as less-than-human, the Caliban could undergo horrific experiments -- grafting, for instance -- that leaves the Caliban even more disfigured. During the process, the Caliban looses all sense of identity and memory, and when discarded as 'failed', he is left with feeling only a sense as if he'd been abandoned by his 'father' and left in a world where he was truly unique, grotesque, and forever alone without a clue as to the workings of anything at all.
If the aim is to capture the psychology of Frankenstein's monster in a character, I'd imagine it could be done with a few of the races. If the aim is to capture the physiology as well, or both, I'd imagine it much more difficult, if not impossible with the given playable races.