To use wireless sync does the PC need to be wireless also

Connected to the same network, I believe. I haven't used it. Device should be charging as well.
 
No, PC does not have to be connected wirelessly. Just connected to the same network/router. And yes, your phone needs to be plugged in, on charge, to keep your WiFi turned on which will allow it to sync while is sleeping (and charging).

Sent from my HTC Surround using Board Express