Place large sheet of waxed paper on clean kitchen towel; set aside. Spray 15x10x1-inch pan with cooking spray. Line with parchment or waxed paper; spray with additional cooking spray. Dust evenly with flour.
Beat eggs in large bowl with mixer on high speed 5 min. (Eggs should be frothy and lemon colored.) Add cake mix, water and oil; beat on low speed 30 sec., then beat on medium speed 1 min. Pour 3-1/2 cups batter into prepared pan; spread to evenly cover bottom of pan. Gently tap filled pan on counter to remove any air bubbles. Spoon remaining batter into 6 paper-lined muffin cups.
Bake cake and cupcakes 15 min. or until toothpick inserted in centers comes out clean. Immediately invert cake onto prepared towel; remove pan. Carefully peel off parchment. Starting at one short side, roll up cake and towel together. Cool completely on wire rack. Meanwhile, transfer cupcakes to second wire rack; cool completely. Reserve cupcakes for another use.
Beat pudding mixes and milk in medium bowl with whisk 2 min. Stir in 1 cup COOL WHIP. Unroll cake; remove waxed paper and towel. Spread pudding mixture onto cake. Reroll cake; wrap tightly in plastic wrap. Refrigerate 30 min.
Mix cream cheese and sugar in medium bowl until blended. Stir in remaining COOL WHIP. Unwrap cake; place on platter. Frost with cream cheese mixture; sprinkle with coconut. Refrigerate 15 min.