Is it possible, using GuiXT, to create in an SAP screen a pushbutton that will call up a program stored on the PC disc, without having to develop anything at all within the SAP application domain?

Yes, you have 2 options, the second one requiring InputAssistant + Viewer components.

Option 1

Create a gif image that looks like a normal pushbutton (in PaintShop you can use the function Special Effects->Buttonize). In the GuiXT script, display the button with the "Image" command. Use the Start="..." option to start your PC program when the user clicks on the image. You can also pass parameters, e.g. passing a material number with start="abc.exe

Option 2

In your GuiXT script, define a new pushbutton with a process="..." parameter. In your InputScript, use the command
View "abc.exe" to start the exe file. Parameter passing as in option 1.

The second option is a little more flexible, since it allows you to perform other actions in the SAP system before calling the PC application (e.g. create a local temporary file with same data or to call RFC functions first to read more data).