The problem is you'll need enough space to store all that information - I doubt a TM is enough space for 15 laptops to all back up onto.
In order to get the space likely needed, You could setup a mac with external drive array and share that TM volume if you wish - a mini would probably work if it's just TM backup and not frequent file serve stuff.
All depends on how critical this information is. If it is critical stuff, then for that many machines you are going to need more elaborate backup plans.