Hmm, I don't have the rulebook OR codex on me at the moment so I'd take this with a MAJOR bag of salt ;) But if I remember correctly the drone controller gives the drones the Commander's ballistic skill, full stop, rather than his ballistic skill specifically during the shooting phase. Taken as that, I'd imagine that the Commander's overwatch bs would also be conveyed to the drones, as it is still essentially his ballistic skill.
Could still be wrong :3
Chaos Marine - "Where's your god Emperor now!?"
Loyal Astartes - "Right Behind you...."
Chaos Marine - *Turns around*
Chuck Norris with a Powerfist - "FALCON PUNCH!"