Adding POE to Ethernet Board If I was to use the Arduino A000024, would I be able to add a POE MODULE to the board to get a Ethernet board with POE to run my arduino project?
If the pinout is what the Ethernet shield expects, then yes. The rows of holes at an odd angle are designed for a POE board similar to that. I can't vouch for whether the pinout is correct though.  It looks ok, but it depends on the dimensions of the board whether it fits the existing pinout.