WiFi sync with computer connected by cable to the WiFi router?

No, if they are both on the same network, there is nothing special you need to do.

First off it's not a stupid question and secondly it's not on the same network. Your PC is on the LAN, that is one network and you iPhone using wifi is a different netowrk. The iPhone sends a Bootp broadcast on udp port 67. This broadcast will not be seen on the second network (LAN). I searched high and low to find out how to get this to work and there is no solution anywhere. So I decided to figure it out myself. The broadcast will not go across 2 networks normally. Fortunately I have a firewall that allows bridging. It also allows me to keep policy based functions between the 2 networks. The bridging allows the broadcast. After the broadcast it does a multicast on udp port 5353. Then the sync works.

To get this working on your firewall/router look for bridging for that make and model. In some cases there may not be any security between the networks once you do this. This is only a problem if someone hacks into your wifi.