It’s a possibility.
It would fall more in line with the original book version of ‘Through the Looking Glass’ because in the book Alice really does become a Queen. Although, it’s a rather short-lived regency considering both the Red & White Queens invite a great deal of looking-glass dwellers to a dinner party for Alice, where she grows; quite literally – tired of their riddles & eccentricities. ( I think this is somewhat portrayed in the Disney version, although very briefly. In the movie Alice runs away from the Red Queen & her guard to the doorknob where she’s pleading for him to open the door & he informs her she’s just through the keyhole asleep. / In the book she realizes she’s been asleep based upon the fact that she grows in height & proceeds to tell the Red Queen that’s she’s tired of her temper & she’ll shake her into a kitten – which she does. )
// Wow. I really got off-topic, maybe I should just make a new thread in the character section for Alice.