As noted in previous posts, AT split is unlikely to generate a yawing moment beyond the aircraft capability. Also, this may require a significant change in thrust; e.g. recommencing climb, or intermediate level off, to result in clutch-slip.
The fin is more effective at high speed, vs thrust decrease with altitude.
The AP might have difficulty, but depending on roll power (no rudder servo), yaw - roll should be contained by the ailerons, thus maintaining heading - with slip.
LoC would require aerodynamic input; i.e. mistrimmed aircraft (no rudder or aileron AP autotrim ?). It is likely that the control indications with AP engaged would prompt the crew to add manual trim - with the AP engaged. Rudder trim might not be the first choice, particularly if the hand-wheel angle offset was large, indicating the amount of roll restoring force held by the ailerons; thus aileron trim might be applied.
All would be well until the AP ran out of authority - possible sudden disconnect, and / or the crew had to fly an out-of-trim aircraft without the normal zero-force wheel centre reference - requiring offset wheel force and position to maintain wings level.
I recall that a 737 suffered an upset, similar circumstances, but due to gross fuel imbalance during cross transfer (the aerodynamic / mass disturbance). The AP failed to fly a LNAV turn so the crew disconnected - surprise, big roll, high hand-wheel forces required to recover.
Searching (web and memory) for incident; probably UK AAIB investigation report - 20yrs ago?