It would make a lot of sense. A full grown man or woman with no memories of who they were (new game), capable of making improvements to his or her abilities (perks), and becoming tougher or more resilient over time (leveling up)? Fallout 3 gave us glimpses of our childhood, while New Vegas explained our lack of memory through a bullet to the head. Being an Android allows us to look just like everyone else and it explains so many of the game's core mechanics in a "natural" way. Plus I think it'd be a good way to force us into the conflict between the Commonwealth and the Androids. Also, it'd be nice to choose whether we want to strive to be human or just be a badass robot.
Let me know what you think of my first post here on these forums.