In theory, it would probably work provided that there is a wireless router somewhere on the network, but I wouldn't trust it to be reliable.
You definitely need a router somewhere on the network if you want to use phones, tablets or laptops though. Home routers provide a service called DHCP, which ensures that every device connected to the network has a unique IP address on the network. Without DHCP, the CDJs will probably still work - I assume they have some sort of fallback system to negotiate IP addresses amongst themselves if no DHCP server is present - but your laptops, phones and tablets don't have that sort of fall back. Without the router, the CDJs might see each other, but other devices won't.
In short, it's probably much easier and more reliable to buy a dedicated router and bring that. Leave the network cables connected at the CDJ end so that you don't wear out the port, and just plug/unplug the router end when you need to do so.