Yes this is possible. My way: install ioBroker including web-adapter and VIS environment.
Then install Firefox-ESR (Version is important!) and start it in an X-session.
In ioBroker you should create a page with VIS. On this page you can integrate any mopidy web-client in an iframe widget.
From there you can control it with the touchscreen.
It’s also possible to directly control mopidy via the MPD adapter here.