Place chicken, onion, celery, broth, thyme, salt and pepper in a 6-quart slow cooker. Cover and cook on low for 5 to 6 hours until chicken reaches 165°F and pulls apart easily.
Transfer chicken to a clean plate and cover. Turn the cooker to high, replace the lid and heat the broth for 15 minutes.
Stir in frozen noodles, separating them gently. Cover and cook on high for 45 to 60 minutes, stirring after 20 and 40 minutes, until the noodles are tender through their thick centers.
Pull chicken into large pieces. Fold it into the noodles with evaporated milk and peas, then cover for 10 minutes until chicken reaches 165°F and peas are hot.
Divide among 6 shallow bowls; the noodles should be coated with thick sauce rather than floating in a large amount of broth.