First the bad news: after trading for and buying runes at Montero, testing has confirmed that Voice of the Dragon is affected by the bug; see attached screenshots 1 and 2.
Next, the great news: as already mentioned by lostkiwi, there is a workaround.

All you need to do is close King's Bounty: Armored Princess totally, then open up the game again, and magically the appropriate morale bonuses would show; see attached screenshot 3. Note that it is not enough to just reload the save file; you must really shut down the KBAP game and just open it up again.
So now there is really no reason not to use droids.
Of note here is that morale effects conferred by other units are not affected by the bug at all. This is the reason why in my game the morale bonus to other undead troops by black knights still show, and in lostwiki's testing the Dragon Despiser trait of Royal Griffins still gives it morale penalties when dragons are in the army with it.