MF only affects the quality (normal/magic/rare/set/unique) of an item. There is no evidence to support that MF or increase of player characters has anything to do with essence drop rates.
I'll put the drop rates below in case you want them. The drop rate actually changes based on if you're killing them for the first time or not.
At players 1 drop, chance to drop 1 essence:
Andariel Non-Quest: 1:14
Andariel Quest: 1:9
Duriel Non-Quest: 1:7
Duriel Quest: 1:5
Mephisto Non-Quest: 1:17
Mephisto Quest: 1:15
Diablo Non-Quest: 1:17
Diablo Quest: 1:15
Baal Non-Quest: 1:17
Baal Quest: 1:15