Does the license server function as a site license?

In other words, we can install as many copies of the app as we wish on our LAN, but licenses would only be issued up to the number purchased – similar to Autodesk’s license model?

Yes the Network License works the same as Autodesk products, in that a user takes a license each time they start Revit, one license is taken per-a-user for as many Revit sessions and versions open as they like.