Can Linux running under VM handle graphical applications?

Absolutely! Even though the mainframe itself typically lacks graphics display hardware, Linux can use the X11 network protocol to interact with a remote graphical display on another Linux or UNIX system, or on a dedicated X11 terminal.

Many graphical applications, especially games, animation, or photorealistic rendering tools, are inherently compute-intensive and therefore may not be good choices for a mainframe hardware platform. In general compatibility terms, though, most X11 graphical programs work fine on Linux under VM.