Just to be clear, the Z3C must connect to the Internet either via a wired Ethernet connection via its WAN port or via a cellular connection. It can't connect to another WiFi network in the house for Internet access using it's built in WiFi capabilities.
If you can plug the WAN port of the Z3C into the Ethernet port of one of these existing WiFi APs and get "ordinary" Internet access - that is fine.
The WiFi in the Z3C is only for clients to connect to.