A utility for Wifi Controllers (as far as I know) is to facilitate configuration to all APs and in some cases (I think) configure roaming between APs.
Depending on the manufacturer, a Controller is not necessary. I think I remember that DLink has some APs that work without a Controller. The ones you have, I don’t know.
All APs can be connected to a Switch and the Switch to the RJ45 interface of the IPFire. But if you have a controller, apart from giving it POE (possibly) it will facilitate the configuration of the APs.
If it is the IPFire that gives DCHP to the APs, perfect, you will have vision of the equipment that is connected. In the event that the DCHP is given by the AP / Controller, it will have to allow the connection to the WAN interface (since it may be NAT) of the AP / Controller.
Each installation of this type is a world and you have to be very clear on how to put it.
I hope I have explained. If someone who knows more about this type of facility wants to contribute their point of view, they are invited.
Sorry for my english, is Google Translator.