Bring 2 quarts water to a boil in a large saucepan; reduce heat to medium, and simmer. Add shrimp; cook 3 minutes or until done. Remove shrimp with a slotted spoon. Add scallops to pan; cook 3 minutes or until done. Drain; cool 10 minutes. Combine shrimp, scallops, celery, and next 5 ingredients (through avocado) in a large bowl; toss well.
Combine cilantro and the next 6 ingredients (through chile paste) in a medium bowl, stirring with a whisk. Add cilantro mixture to shrimp mixture, tossing to coat.
Place 1 cup trimmed arugula on each of 6 plates; top each with about 1 cup seafood and avocado mixture.