Make a session choice for the GDM login menu.
In the folder /usr/share/xsessions/ make a file foo.session in this format.
[Desktop Entry]
Encoding=UTF-8
Name=
Exec= /URI/bar.sh
Icon=
Type=Application
In any folder, put bar.sh
#!/bin/bash
foo.bin &
exec bar.bin
To carry over GNOME look and feel settings, include
gnome-settings-daemon &
To draw a tiled-image wallpaper without using Nautilus to draw and run an actual desktop, run
feh --bg-tile foo.png &