I think it should "just work". The added load would drive voltage down, so the inputs the ECU gets continue to send the right message. So long as the alternator has enough capacity to meet the demand...

Yeah if a manufacturer wanted to hold off on drawing a higher load to recharge the battery until after the car was warmed up they would just do that by lowering the setpoint. If you try and draw higher current from it it would still meet that lower setpoint.

I doubt that was the case for the depicted 1992 Chevrolet Astro Van.