@Athmos is right, it works that way, as he described.
But, I have seen a bug about Mobile Base - it gets stucked after clicking 'move drones in' , 'move drones out', 'go different spot' and custom randomization of that operations - the finish product of this is = Mobile Base get stucked without any drones - they have vanished (but not at all, only on that vehicle). I have seen that on fight with ground-miner aliens, when I have to move around map and destroy them. Reassigning a drones and assigning them again to different Mobile Bases, and moving them made me crush 1 of 5 that wheel-bases, and there was nothing I could make to move that vehicle, only salvage.
But, again, there is a bigger thing - when You have a lot of drones assigned to vehicle, and, as
@Athmos said before, i click to move the vehicle, the drones in first phase starts to come back to car. Sadly, the signals to drones to come back stops quicker that drones has opportunity to actually came back in, and some of them leaves there where they were staying because Mobile Base started to move and didn't wait for them.
Sad, pour, abandoned drones
