A/P's will control rudder trim
In a 3 channel approach the A/P's control the rudder itself not the rudder trim , thus when two channels drop out, for whatever reason, the rudder reverts to its trimmed state and some fancy footwork is required to avoid rolling on ones back.
Personally I prefer to fly a single channel approach when on one engine and keep control of the rudder myself but depending on your MCP fit that may not be an option for you.