I haven't tried (I don't own any of the GMS2 mobile export targets) but as far as I'm aware the engine doesn't use any Windows-specific functions.
I think the biggest stumbling block would be lack of touchscreen support... if you go with the "virtual gameboy buttons" approach a lot of the mobile emulators used to play Pokémon games seems to have picked (where there's a D-pad and A / B / Start / Select buttons on the screen and the rest doesn't respond to touching) this is probably not a huge issue, but if you want full touch support for menus, you're going to need to add that yourself.
On the plus side, all GUI elements are defined with basically the same logic and are put in a single array, so on a touch event (i.e., Global Mouse Pressed) you can basically loop through all elements in the currently active menu and see if any of them are in the target zone: