Possible, but I'm not sure I'd call it probable.
The common thread in the fiction is the grey, featureless locale the personalities described are, presumably, written to by the JackBNimble program. The Captain Chaos backup, for lack of a better term, seemingly had a flaw in the recompile process, as the imprint was self-aware unlike the others. But the Alice snippet showed no signs of her imprint being stored at all, as her story ends on the note that she's going down the rabbit hole.
I guess time will tell. I for one fervently hope she's still around in some way, shape, or form.