There is quite a few ressources explaining how to set up a FOG server .
Once you have managed to do that - taking care of possible DNS challenges - you can go forward and either make a live-boot image available or go the way of building your own image and then making that available to your computers in the network. This could probably be done in a “live” way as well.
As Sebastian said this scenario is not what FOG was built for, but it is rather easily imagineable to build something along those lines.
Maybe somebody else has already set up something like this, but the best way will probably be to read the wiki links and tackle it yourself. :)
The developers here are extremely friendly and helpful, but its always easier to help with specific problems and steps than answer a sprawling: Tell me how to set up FOG and do X or Y.
Get your feet wet, dive in and everybody will be happy to help if you get stuck :)