No, Cecil comes with the same equipment when he joins permanently. Although, you can de-equip him in Ceodore's Tale and he'll still come equipped with the King's Sword and the rest again. That means you can get two sets of his unique equipment if you want.
Like FFVI? Read mah prequel, The Sands of Time! http://www.fanfiction.net/s/6209029/1/Final_Fantasy_VI_The_Sands_of_Time