I haven't messed with anything like this personally, but yeah this should absolutely be possible! I don't see why not, and I'd love to see it happen.
An additional tiny thought:
The Shortcut option inside the Button Properties window:
When there's a Shortcut set up, that key press will 'click' on the associated button, and it allows for things like WASD navigation for your players with keyboards in front of them which might suit this kind of game well. (Though also having on-screen buttons is ideal for mobile players.)