Yes, when the A/C is running, the IAT will potentially go up. Because the condenser for the A/C is in front of the charge air cooler. Again, normal. Typically this heat load isn't *that* bad for that long since once the heat is removed from the cabin the compressor's duty cycle backs off and the high side pressure is not as high. When regens happen, the fans run on high no matter the coolant temp or refrigerant pressure. This is to help keep air moving under the hood.
Not sure why, maybe they did not think it necessary OR felt the A/C would be running anyway, but the IAT has no impact that I know of on fan operation, despite the fact that the fans do pull air over the charge air cooler just like the condenser and radiator.
You'd have to get some datapoints for "normal" IAT on CJAA engines to get some idea of what is going on here. But again, I don't feel like that is the reason your engine is stalling.
The circulation of coolant, refrigerant, and the charge air passing through should be fairly dynamic but predictable.