No. You would see the target in lock losing no HP, but still getting a hit-message (you can check these in your log).
However, as you said yourself: Misses can always happen randomly even if a drone is already in orbit of a Battleship sized target. If the target moves “south” and the orbit of the drone is at one moment in the direction “north”, the transversal can still be pretty high, resulting in a lower hit chance in the tracking formula. Also it can be that the drone gets out of it’s optimal range for a few seconds at the peak of it’s orbit that is at the exact opposite direction where the target is moving to. And since drones have a very low falloff-range, you might see 1-2 misses before they catch up again to their target.
I especially notice this in the Abyss, where some advanced battleships can go 300, 400, or 500m/s - or even a lot faster when entering a tachycon cloud.
So, while pretty rare, yes, even medium drones can occasionally miss a battleship. Note: they can also occasionally do “penetratiing”, “smashing” and “wrecking” hits, which offsets their rare misses on average quite well.