Definitely!

She's so much like a child an interested in the world, I guess she'd love cute anime girls....well...I mean, since the way she acted all cute on the snuggly duckling rebels, and she pretty much sees something good in everyone from my point of view, why WOULDN'T she like anime?

Also Mulan, she seems so intelligent, like the way she knew about the fireworks and the mountains, may have some relation to physics. So since maybe the way she was interested in all this chess and physics (like me) might be by curiosity, which will find her way into the world of anime, getting more curious about all the types of it and style.

This is weird I know, but i'm trying to back up all the possibilities from my senses, and my senses are telling me Mulan and Rapunzel will only like Anime.

She seems like the type.

I can see her reading a shoujo manga... A cute love story!