Bring a large pot of lightly salted water to a boil. Cook orzo in the boiling water, stirring occasionally until cooked through but firm to the bite, about 11 minutes. Drain and transfer to a large bowl. Add mandarin oranges, pineapple chunks, crushed pineapple, and maraschino cherries to orzo.

Combine juice from mandarin oranges, juice from pineapple chunks, juice from crushed pineapple, sugar, eggs, and flour in a saucepan over low heat; cook, stirring often, until sauce is thickened, 5 to 7 minutes. Remove sauce from heat and cool, about 30 minutes.

Pour cooled sauce over orzo mixture and toss to coat. Refrigerate until flavors blend, 8 hours to overnight. Fold whipped topping into orzo mixture before serving.