There have been several Alice musical attempts, most of which have folded on the road to Broadway. The most notable being the Disco Version called "Alice" with Debbie Allen as Alice, Cleavant Derricks as the Caterpillar, and Alice Ghostley as the White Queen, that shuttered in 1978 on the road.
Honestly, if you can find a way to work it, it could be amazing, but as someone pointed out, it's a meandering story, with lots of characters, and doesn't lend itself to musicals well.
There is one play version though, that I wanna say was set in a mental institute...and it's a group of 6-7 actors, and one plays Alice, the others trade out roles, and as she leaves Wonderland, they do the entire Rabbit Hole sequence backwards. Now THAT was impressive.
http://www.youtube.com/huskcharmer