The vehicle HVAC fans would still turn off when cranking. The momentary switch does not connect the house battery to the chassis run circuit; rather, it switches the control line to the battery combiner solenoid from the chassis run circuit (non-pressed) to a house battery circuit (pressed).
This does imply having a pretty heavy gauge wire between the solenoid and the batteries, and a sufficiently beefy solenoid. On my motorhome I think it's 2 gauge wire or so, with appropriately big fuses at either end.
