Airplay over wired network? I intend to buy a MacBook Air.

I already own an AirPlay enabled receiver/player from Denon. It features both WiFi and Ethernet network interfaces.

Will AirPlay work over a wired (Ethernet) network (no WiFi at home).
Yes, it will work as long as both the MacBook Air and the Denon receiver are on the same network segment. Your Air will need either the USB or Thunderbolt adapter to connect to ethernet (the latter provides Gigabit speed as well as supports jumbo packets) directly.

You can have many iOS devices and the Air also connect over a wireless bridge and they will see the receiver that is connected via ethernet to the main network switch.