I've been playing the mobile version of Minecraft for a few days now, and have yet to see an underground cave system. Are there any generated with the terrain, or is it all solid ground?
I've spent the better part of an hour now searching for a source to confirm my answer, but I can't find anything. However with that said:
It's based on Minecraft Classic, so I doubt there would be, especially considering the world has an end just like the original Minecraft Classic on PC (on which there are no caves).
Add that to the fact that I'm yet to come across a cave system as well and I'm pretty sure there aren't any.