Correlated Equilibrium for Rock Paper Scissors
No, the unique Nash equilibrium is the unique correlated equilibrium by a general property of two-player zero-sum games pointed out in:  


  Forges, Françoise. "Correlated equilibrium in two-person zero-sum
  games." Econometrica (1986-1998) 58.2 (1990): 515.,


For every action of player 2 that is played with positive probability, the conditional distribution over player 1's actions is an optimal strategy for player 1 and vice versa. Since optimal strategies are unique in RPS, the conclusion follows.