Can I imprint my Commander onto Mimic Vat, and still take it back to the Command Zone?
No.


  607.2a If an object has an activated or triggered ability printed on it that instructs a player to exile one or more cards and an ability printed on it that refers either to “the exiled cards” or to cards “exiled with [this object],” these abilities are linked. The second ability refers only to cards in the exile zone that were put there as a result of an instruction to exile them in the first ability.


There are no cards in the exile zone, so there is nothing to copy.