Can the Wii be controlled by an AMX system? It obviously has an ethernet port.

Obviously, you have to buy a USB adapter to get that ethernet port otherwise it operates via WiFi. If you would like to control a Wii with an AMX system, you should post the results here, also you should post your reasoning since I cannot seem to find one.
If you want to integrate it in a system for your system or a customer's, just hack open a USB cable, hook it up to the back of the Wii and then plug the Hot and Ground leads to a voltage sensor. Then program your system to run the macro for the Wii in that zone when that port goes high, aka someone turns on the Wii. This is great for kids who are too young to be handling a remote.

Thanks, I'll have to try that using an XP-8. Turning on the entire system for gaming with only the Wii remote would be perfect for many people.

The above advice does not work because the USB port is still live when the Wii in powered off in standby (amber light). You would have to instruct the kids to hold the power button on the Wii for 5+ seconds to turn off the USB (red light).

XP-8 plus SPS-1 works great for the Wii if you split the Yellow/Green. On a PS3 the red/black wires in the USB will work for the idea mentioned above except the USB is on the front.