Cook noodles in a large Dutch oven according to package directions, adding broccoli during last 3 minutes of cooking time. Drain mixture; rinse well with cold water. Drain well.
Meanwhile, heat canola oil in a large skillet over medium-high heat. Add chicken; sauté 5 minutes or until browned. Add mushrooms, bell pepper, and garlic; sprinkle with 1/4 teaspoon salt. Sauté 2 minutes; remove from heat.
Whisk together sugar, next 4 ingredients, and remaining 1/2 teaspoon salt in a large bowl. Add noodles, broccoli, and chicken mixture; toss well to coat. Divide salad evenly among 4 bowls; sprinkle with green onions and sesame seeds.