They'd be a poor call centre if they couldn't route calls to when they can best deal with them, and put them in a queue when all the agents are busy. Yes they will have an "exchange" at the very least.
call centres generally work on a particular server of their own.they have a tie up with phone companies which provide their server for landline calls.
Presently Avaya is used in most of the call centres and it has many facilities inside it which includes call bagging and tracking as well.
Call centers have a setup of servers and high defined routers which make easier for them to communicate to the different countries without any consession.