I attempted to use a skeleton mob spawner at a y of about 16 to farm arrows and bones using a simple drowning trap, however, the skeletons persisted well over a minute, and were clearly not drowning. I an attempt to 'update' them, I started fights amongst the skeletons and punched them, but to no avail. However, when I exited and reentered the world, some of the skeletons were suffocating in the block above the water and the ones who were not were drowning properly.
I replicated my drowning trap in a separate world on the surface but instead of using a mob spawner, I used eggs to spawn in the skeletons, and they drowned as intended in a short time.

UPDATE: The drowning location of the skeletons is flowing water from a source block one block away. This appears to drown zombies, players, and egg spawned skeletons, but does not drown mob spawner skeletons. If the drowning location is a source block however, the mob spawner skeletons still drown.