No, the Red Sox should not resign Jacoby Elsbury, because they are strong enough without him. Elsbury was not one of the best players in the Red Sox's recent success. They are capable of returning to the World Series without him, and there are better players who contribute more in team situations.
No, the Red Sox can not resign Jacoby Elsbury since he is no longer a member of the Red Sox. On December 7, 2013, Jacoby Elsbury officially became a member of the New York Yankees. Since they cannot resign Jacoby Elsbury then by default the answer to this question is no.