The emergency start switch does not interrupt the run circuit on the chassis in general; it's only controllign power to the solenoid that connects the batteries. One option for where it gets its power is from this run circuit, the other is from the house battery. The rest of the run circuit, and the key switch's control of it, is not changed.
The blower is stopped by the key switch alone. The combiner solenoid is also controlled by the key switch if the emergency start switch is not pressed (and, apparently, if the DUAL switch is engaged, provided you have such a switch...I don't on my motorhome). The idea is to use the existing circuit, controlled by the key switch, to also control the solenoid except for the odd circumstance where we want it controlled independently; so we put in a switch to select between the usual control via the run circuit from the key switch, or the house battery for what amounts to manual control.
If the emergency start switch is not pressed, then the batteries are indeed not connected together when the engine is cranking, and the chassis and all its appertenances is getting power solely from the chassis battery. Once the key is released they are (re)connected together, provided the DUAL switch is engaged if you have one, and the alternator charges both batteries.
If the emergency start switch is pressed, the two batteries are connected in parallel as long as it's pressed, regardless of the key switch position, and the starter and other chassis circuits can get power from both while cranking the engine. The rest of the chassis circuits are still controlled by the key switch as normal; electrically, this is precisely equivalent to hooking up jumper cables between the two batteries.
