It depends upon the files you are streaming. If you have 160kb/s MP3s (rather standard import from iTunes... this is all legal music isn't it?) that's roughly what you will be streaming (plus or minus due to the buffer). OK, it's a networking problem, so there are MANY variables (like routers, switches etc. that would solve most of these problems) but lets say worst scenario... you are all on the same subnet, connected via a very dumb hub (no routing).
Think about it this way... If you are all on 10 base T ethernet...
Again, most of this is theoretical, and would probably not give you this maximum.
10 megabits/s = 10240 kilobits/s
So... you can see that you would totally saturate the network with 10240 kb/s.
So 10240kb/s divided by 160 kb/s, you get 64 streams.
Again, this is theoretical... and I would guess that at around 60% capacity, things could start to go "wonky".
So, 30 or so streams would be safe, but chewing up a considerable amount of the network.
OK, now, if you are on your own router (say three rooms are all connected to their own router that in turn is connected to the backbone of the school, NOBODY would see the traffic beyond the router.
It also doesn't take (hardly) any space to host the library.
PS. Almost nobody is is using hubs anymore... with a router, you could stream as many as you wanted to... they would all be independent of one another internally.