Unfortunately, no. Elite Arcanist has “linked abilities,” which means the second ability only refers to cards exiled by the first ability. You may be thinking that the first ability DID exile the other card before the wizard got exiled! However, there’s another important rule that explains that a card becomes a new object when it changes zones. In the case of Cloudshift, that means when the card moves to exile, then moves back to the battlefield, it loses all memory of its former self, including any formerly exiled cards. Basically, it would be similar if you were Leonardo Da Vinci in a former life, but were reincarnated as yourself. You may be represented by the same card (or spirit/soul?), but you don’t get to start out with all the knowledge you accumulated in your former life. The new Arcanist doesn’t have anything linked to it, except whatever you might exile as the new enters-the-battlefield trigger resolves.
The only way to double up on exiled cards is with Strionic Resonator! If you copy the triggered ability and exile two cards, you get to cast both of them when you activate the Arcanist’s ability, but you’ll have to pay for the full CMC of all exiled cards to activate the ability.
Today’s Rules Tips written by Josh Stansfield
P.S. Happy 2014!!!