Just FYI, a real Mac (like the Air) can boot off the remote disk when shared from a real Mac I believe. This is one of apple's officially supported ways to reinstall the OS on an Air.
Minis do support PXE boot (network boot), and as I recall OSX server has tools for making PXE/network boot images so that real Macs can do network boots (like in a school computer lab). I have set up PXE boot at work to deploy operating system installs to machine with blank hard disks (XP and Vista, not OSX of course).
I am way out on a limb here, but I guess theoretically you could make a network boot image that would support a mini as long as you have OSX server available. The apple tool creates the PXE image for you, so I would guess you'd have to open and modify the PXE image to include a different boot loader/kernel/kexts or what have you. I think this would be an enourmous amount of effort just to avoid hooking up an external drive from time to time.