In theory nothing should happen as it should self-negotiate and will probably run off the 12V instead of POE as it should respond to the first one that gives power.
But I wouldn't trust the camera and would recommend not doing it.
I obviously can't speak for every IP camera on the globe. The Dahua and Hikvision models I've had all have a blocking diode on the 12 volt input, which means that the camera's POE-to-12volt circuit cannot push out to whatever is connected to the 12 volt power connector. It would be good design practice that the POE-to-12volt circuit would be the same, that it wouldn't allow power from the 12 volt connector to be pushed in it, but I have not verified that. The most probable case is that the camera will pull its 12 volt working power from whichever source has the highest voltage, and if the voltages are close, it might share the load between the two. But why on earth would you want to provide both power sources?
