Does the looting enchantment affect drops from players?

The answer to your question is No, killing players with a looting sword does not affect what they drop from their inventory.

Looting only affects "spawned on death" drops, and not "it's what I was carrying" drops. A "spawned on death" item would be something like rotten flesh; the zombie wasn't actually carrying it in its inventory, but it still dropped anyway. Using a looting sword can make it more likely that rotten flesh will drop, and more of it when it does.

Now if you gave a zombie a stick then killed it, it will ALWAYS drop exactly one stick - this would be a "it's what I was carrying" drop. Killing a zombie with a looting sword would have no affect on how many sticks this zombie would drop (rotten flesh still drops in addition to the stick).

Players do not have any "spawned on death" drops, with the exception of Notch, who drops an apple on death. Though I don't have any data to back this up, I'm fairly confident that if you killed Notch using a looting sword, it would be possible to obtain more than one apple.

The looting enchantment (according to the minecraft wiki) has the following effects:

Mobs can drop more loot Increases maximum loot drop by +1 per level. Increases chance of rare drops by +0.5% per level (i.e., 3% at level I, 3.5% at level II, and 4% at level III).