Do AN-X2-AB-DHRIO gateways work with redundant ControlLogix processors?

Yes, the AN-X2-AB-DHRIO gateways are capable of communicating via EtherNet/IP with a ControlLogix system that is configured with redundant processors.  Due to the nature of the redundancy, the AN-X itself does not care WHICH processor it is talking to, it is programmed to talk to a processor at a certain IP address.  So long as it can do that, it should work just fine.