I'm not very familiar with the Arduino wired Ethernet controller but I looked through the documentation and didn't see anything about it being able to sense link state or not.
One thing you could do is connect the Arduino's serial port to the console port of the Cisco then configure "logging console" on the vty and "logging-event link-status" on the Ethernet port, then have the Arduino parse the console log.
Alternatively, you could set up the console port with a reverse telnet and write a simple parser on the Arduino with something like "R1" to turn the relay on and "R0" to turn it off, etc.
Hope this helps.