Alice is a mystery, but even if she did that, she's still semi-divine, so by now even if she started out in a doll's body, it's become real enough at least to be together with Marisa. Also, no matter how you look at it, she's probably immortal. Either a human that Shinki turned into a youkai (magician type) or a doll that Shinki breathed life into, either way, Marisa even mentions the possibility of becoming a youkai herself, so she probably isn't.