A few things here; First, my Itasca has the step wired to the chassis battery, not the house battery. Turning off the house battery has no effect on it.
Second, turning the ignition on, regardless of the step switch position, overrides the step switch and will raise the step when you close the door.
Next, if the switch is turned off, the step will STAY in the position it is currently in, regardless of whether you open the door or not. In other words, turning the switch off when the steps are retracted will keep the steps retracted. Turning the switch off with the steps extended will keep the steps extended, regardless of opening or closing the door.
HOWEVER, there is an exception: The "last out" feature (also known as "auto extend") will override the switch's "off" position ONCE after the ignition has been turned off, and extend the steps the FIRST time you open the door, and then retract when you close the door. Subsequent opening/closing should have no effect; the steps should remain retracted.
Here is a link to the service manual. Scroll down to page 32 of the pdf, and you can read exactly how the system works.