Wireless sync of iPhone to wired mac Home network set up: Incoming line from the world goes to an Internet switch with local Wi-Fi. One of the switch lines runs to a second switch at the other end of the house. Most of our devices have hardwired connection. I really don't want Netflix on the AppleTV to fight for bandwidth with my laptop and my wife's iPad.

I also have a Mac Pro that is the center of my computing life. The Mac Pro has its Wi-Fi switched off.

I've told my iPhone and Mac to sync wirelessly. This isn't happening.

Do both computer and iOS device have to be using Wi-Fi for wireless sync to happen?

Is Apple networking smart enough to do the right thing if I have my desktop with two live ethernet connections. (This was a good way to get in trouble with just wired networks. Spanning tree and all that to shut down the extra link.)
Bonjour driver that is used to handle Wi-Fi sync between OS and iOS device requires WLAN connection. 

If your Mac doesn't have Wi-Fi enabled, you may need some additional configuration. Check this article: https://discussions.apple.com/thread/5092691

Also, Bonjour requires multicasting, so you will need to configure it if you have a mesh network. Check this article if the previous one won't help:
https://superuser.com/questions/328205/how-can-i-get-bonjour-to-work-over-my-wireless-network

Not sure about this one, but could be also useful:
https://community.cisco.com/t5/switching/routing-multicast-apple-bonjour-specifically-in-routed-vlan-d/td-p/1504513