Is it possible to add some 'PXE Network Boot' option to GRUB?

Yes, you can add a (i)PXE Launcher to Grub.

For dpkg-based systems like Debian&derivatives: Only apt-get install ipxe is required

I would expect other distros to have integrated it as well fairly comfortably.

==> A "PXE Boot" menu entry will exist on next reboot.

In case you want to know inner-working-details:

The post-install hook scripts automatically adds an iPXE entry to the grub configuration, using the "template" file /etc/grub.d/20_ipxe.

You end up with an entry like the following in /boot/grub/grub.cfg

menuentry 'Linux NetBoot Environment' {
  set root='(hd0,1)'
  <More, less important options>
  linux16 /boot/ipxe.lkrn
}

This just means, that instead of a (linux-)kernel, grub gives full computer control to another "simple" program, in this case ipxe.lkrn. MemTestx86 is launched in basically the same way.

The PXE Stack is software normally stored somewhere on the main-board. Just in this case we load it from somewhere the drivers from GRUB can access.

Example of a usage scenario:

You will want to install a basic GRUB on the drive, having the PXE entry first, and a fall-back on Position 2 to local chain-boot from (say) Partition 1.

The configuration iPXE would use will then depend on the files residing on your boot-configuration-server. There you will make the default, first menuchoice "Boot from local Partition 1", then more choices (Boot-AV, SuperGrub, Debian NetInst...).

==> Your Users normally don't touch anything until they see the Graphical Login Prompt from the local Installation.

Boot-Sequence: GRUB - iPXE - OS-in-Partition-1 (Fallback to OS-In-Partition-1, if PXE unsuccessful)

==> Physically present at the PC, you could choose other Boot-Options.

==> Not physically present at the PC, you can change the server-side PXE configuration to "one-off" boot another choice than the default.