Sorry I may have parsed the question in the opposite direction. If what you want is using Jolla programs on a X11 server such as the one on a GNU/Linux desktop then that's just not possible. However there's already something for that which uses VNC instead of X11 -- https://github.com/mer-qa/mervncserver

On the other hand, if you want you want is to run X11 programs on the Jolla, that's what Xwayland does, but without touch input as mentioned (either an issue with the oldish version of wayland in the Jolla , or a qtwayland incompatibility -- will look during weekend).

Xwayland also has two modes:
- "normal", in which it behaves similar to Xephyr or Xnest: a single new Wayland window is created in which all X11 programs run. You can use your own window manager inside this Xwayland window (with titlebars, maximize/minimize buttons, etc).
- "rootless", in which a new Wayland window is created for each X11 toplevel window. So you can basically switch between X11 window using the "sailfish" gestures. Unfortunately, we'd need to write a new X11 window manager for this, and take into account that we'd need to handle special windows such as menus on our own...