@Datsys You have both a technical and legal question in your post that will require a fire dance to navigate well.
On the technical side, it is possible to configure FOG in a mobile deployment server mode. Whereas you can have FOG loaded on a portable computer and take it from site to site to deploy images. Its best if you use onboard storage for the images but it would be possible to use a portable usb drive but your downloading performance would be not good because of the bandwidth. If you used a high speed usb-c attached drive then performance would compare to onboard storage. One issue I see is that to properly network boot target computer for imaging you will need certain network infrastructure changes to make it work. This is modifying your dhcp server to send out the boot server (FOG server) ip address and boot file to load. While the fog server is on site this will work perfectly, if the fog server is at a different site not so much. You can mask this issue by installing dnsmasq on the mobile deployment server so that only the pxe boot information is sent out while the fog server is on site. This can also be problematic, but it is a workable solution.
The MS Windows/legal issue is a bit more complicated. For OEM licensed computers you are not allowed to create a golden image (customized image with additional software loaded) and then capture and deploy it to multiple computer. The EULA requires a volume license key for this. You can deploy images only in the OEM format and then after that is deployed add on custom software on top. To be able to deploy an OEM image (legally) You can either use FOG to share the ISO image to the target computer, or what I’ve done in the past is take a development machine and install Windows 11 on it, but only to the point of the first reboot. You MUST stop the system from booting on that first reboot. That first reboot is the transition from WinPE environment to the Windows Setup/OOBE process. Now capture that image at the first reboot and deploy with FOG. This is still inline with the OEM EULA because you are not altering the image only cloning it during the middle of installation. When you deploy the image to computer #2 WinSetup/OOBE will continue to run. Now at the end use FOG to install custom applications and your done.
I can tell you getting a VLK key and image is a much simpler solution. I don’t know what M$ current licensing is, but it use to be you only need to purchase 1 VLK key for all of the company’s computers to use the VLK key. You needed 5 licenses to reach the minimum order so for small companies that had a windows server and windows workstations we would purchase 1 VLK key and 4 widows servers client connection licenses, cause you can always use server connection licenses. Just let me repeat I don’t know what MS current licensing model is so this may be old information.
Just to wrap up:
Can you create a mobile FOG deployment server? Yes. You will need to be really familiar with Linux to do this though.
Can you repurpose all of these unused windows 10 computers as FOG servers and leave then connected to the customer’s network, Yes (a bit better idea).
Can you deploy Windows 11 with FOG, yes (until MS break this too).