Commander damage from Mimic Vat token?
No. The Commander rules state (CR903.3) state: "[Being a commander] is not a characteristic of the object represented by the card; rather, it is an attribute of the card itself. The card retains this designation even when it changes zones." and drives the point home with the last example: "A permanent that's copying a commander (such as a Body Double, for example, copying a commander in a player's graveyard) is not a commander."