Yes. Once your AirPort Extreme is set up, it will work with any wireless client, so long as they are capable of joining the type of network set up by the Extreme.
Think of it this way; whereas other routers' admin utilities are browser based and accessed via IP address, the Extreme requires a program to be installed. And just like you don't need to connect to the admin utility from every computer that joins other routers' networks, you don't need to install AirPort Utility on every client computer. Just the administrating computer.