Zobrist's eligibility won't help you if he is your only 2B. He can't be moved around to other positions if there is no other second baseman on your team. And I agree that I wouldn't have him as a starter either until he shows he is back from last season's big dip.
At very least you could use a 2B/SS cover cause you have no back-up in those positions at all. Doubt if Aviles or Theriot are still available but maybe someone like Tsuyoshi Nishioka still is? Don't know much about him but he is eligible at both positions and is said to have some decent SB upside as well.