Yes, controllers are supported in the demo.
One thing we have to make clearer that we've noticed though, is that the 'LB' (the button above the Left Trigger) can be used to 'freeze' the play in it's current place to allow more precise movement of the mining laser or weapon with the left stick. It does tell you this in a pop up box in the tutorial, but it's quite a bit of info in that box, and we feel we need to make it clearer, as people miss it sometimes. But it should work fine.