Using GarageBand for MacOS X, I have no difficulty importing and playing .mid (MIDI) files. Indeed, I can even rename .kar (Karaoke) files to .mid, import them into GarageBand for MacOS X and see the lyrics along with the score. Using File Sharing for iOS apps in iTunes.app, I have tried to import .mid and .band files (made from .mid files with GarageBand for MacOS X) using this mechanism. I get no errors but it doesn't seem to work. That is, neither the .band file nor the .mid file are accessible from within GarageBand for iOS as far as I can tell. What should I be doing instead?
As I understand it GarageBand for iOS .band projects can be imported to GarageBand for OS X, but the reverse isn't true. GarageBand for iOS does not import midi files.
The File Sharing section of iTunes doesn't validate the files you put into it, but if the app doesn't like the structure of the file it will just ignore it.