I think it will stay an economic building - it just so happens to span troops if it's destroyed. If a troop (eg: saboteur) walks past the house on the way to a tower, the house won't attack that troop.
Just like Farms which remain economic though they can spawn troops with Kremlin.
Not really, farms with Kremlin spawn defenders once, when destroyed, like factories, barracks, armory, etc., houses spawn defenders continuously just like garrisons or tank depots.