Thanks to hhm, who pointed me at KBOX, I have verified that I can build haskell programs that work on Android.
After hacking on it all day, I've succeeded in making an initial build of git-annex for Android. It links! It runs!
Which is not to say it's usable yet; for one thing I need to get a port of git before it can do anything useful. (Some of the other things git-annex needs, like ssh and sha256sum, are helpfully provided by KBOX.)
Next step will be to find or built a git port for Android. I know there's one in the "Terminal IDE" app. Once I can use git-annex at the command line on Android, I'll be able to test it out some (I can also port the test suite program and run it on Android), and get a feeling for what is needed to get the port to a usable command-line state.
And then on to the webapp, and an Android app, I suppose. So far, the port doesn't include the webapp, but does include the assistant. The webapp needs ghci/template haskell for arm. A few people have been reporting they have that working, but I don't yet.
Maybe this helps: http://forum.xda-developers.com/showthread.php?t=1444792
https://play.google.com/store/apps/details?id=com.madgag.agit&hl=en
I used it and its decent and certainly runs git as a backend (although I havent seen its internals)