If I use Mimikyu's "Impersonation" attack to discard an opponent's Whitney, does that Whitney count for the "draw 2 cards for each other Whitney in your Discard Pile" because you're not actually playing that Whitney, just using its effect?

No, you still cannot count that Whitney towards the number of cards to be drawn because its text only includes any OTHER Whitney in your Discard Pile.

Relevant cards

SM12_245

SM12_96