Yes that works. The powerline adapters are entirely transparent to that layer of protocol. [A more common use is for home networks that have a separate IP address range for a "guest WLAN".

Are you connecting two cables from the router or just one?

Yes ... you should actually be happy that the payload datapath THROUGH the switch is faster than the interface datapath INTO its management engine.

Set your AV1200 pair up, and then add the AV500 adapter in, using the keycode method on a PC connected to one of the AV1200 using the Powerline Utility software.

Unless that switch is multicast capable, your setup is flawed anyway, and adding the PLC just magnifies the problem. The technical feature you're looking for in a network switch is IGMP/MLD...

The powersave feature, although heavily suggested in user forums, hardly ever is the culprit. I've had a Windows PC that couldn't reconnect when waking up from Windows "energy saving" mode. I had to...