If  the IOE controller loses communication to the I/O boards or loses power, the system will still continue to run if there is AC power being supplied to the rectifiers.  However, you will lose your battery back-up if the controller is not communicating with the I/O boards or does not have power so a loss of AC power would bring the system down.

The IOE controller controls the change over from the rectifiers to battery power and the Low-Voltage-Disconnect for the batteries.  If the controller is not communicating with the I/O boards, it would not know when to switch to battery back-up so it would not switch and rely solely on AC power to the rectifiers for supplying the system with power.