Yeah, I'd say that's possible. How you do it though, well there's probably a bunch of different ways.
If it's adding premade parts, then that would be relatively easy (each piece having a unique id number, and if you save those id numbers, then it knows what to change it to look like later.. heck even use a codeword type system or something eg: 924519281 would create a character (hey random character building! lol). You'd have your base character as the collision boxes and invisible and go from there, just attaching your custom character to it.
If there's more going on, like allowing them to actually draw the parts themselves. Well again I don't see that being too complicated really considering it would be pixel art, so you'd basically have a small grid with each piece being on or off and the color being decided by whatever they've selected in the games UI (can reference RGB info) then I dunno, similar method to above for storing the information or even saving the parts out. Not entirely sure about that bit, I've really not looked into the whole saving and loading thing beyond seeing the loading having problems (don't know if those are fixed yet).
I don't think the image editing object will be useful for this though.