Airfoil does not work with ARD, per se, in that ARD isn't involved other than giving you the ability to control the workstation to turn on Airfoil. It could stream the audio on one workstation to a player such as QuickTime Player on another, with or without ARD. It's not something that ARD will trigger unless you take manual control of the applicable workstation and turn Airfoil on and off from your admin station.
I'm not sure, though, that you really want thirty systems all streaming across your network, unless you have a lot of bandwidth to spare. In addition, unless Airfoil has password protection on the streams - it may; I haven't looked into it that deeply - then any of your students could be connecting to each other's streams, something that in my experience could quickly lead to chaos.