No, mesh networks’ APs use WiFi to connect to each other so that eventually client traffic reaches one that can finally route to the wired network. Client traffic doesn’t go through one AP to immediately reach the wired network.

I’m talking about a traditional network where everything is wired together using Ethernet (probably to a switch) so that client traffic on the AP immediately reaches the wired network from that AP without that AP then relying on another one to reach the wired network.

This arrangement is still common today on business networks and was so before the term “mesh” became popular in consumer routers.