Will the drones stop responding if I fly the Vulcan too far away or dock the Vulcan in a nearby carrier?

The drones will have a maximum control range, as you approach that you'll be warned in time to make a choice to return or continue at your own risk. If the Vulcan or the drones exceed that range then they will slowly stop responding until they are completely unresponsive. Simply coming back in range is enough to return them to complete control and causes no lasting damage.