This file is indexed.

/usr/share/xsessions/gnome-fallback.desktop is in gnome-session-fallback 3.2.1-0ubuntu8.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

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[Desktop Entry]
Name=GNOME Classic (No effects)
Comment=This session logs you into GNOME with the traditional panel without any graphical effect.
Exec=gnome-session --session=gnome-fallback
TryExec=gnome-session
Icon=
Type=Application
X-Ubuntu-Gettext-Domain=gnome-session-3.0