I don’t think that Pinocchio was made of a magic tree. I thought he came alive because the blue fairy made him come alive because Geppetto was lonely. I don’t remember. Even if he was made out of a magic tree i still don’t want Geppetto to decide to send him through the tree possibly taking away the chance of sending Snow and Emma through. I just don’t want that to happen.
I think it is possible that people could go through to the real world some other way. I just don’t want someone to be sent through the same tree wardrobe ahead of Emma.