Spray a large slow cooker with nonstick spray.
Place celery, carrots, onion, chicken broth, condensed soups, uncooked chicken, and poultry seasoning in the slow cooker.
Cover and cook on LOW for 4-6 hours or on HIGH for 2-3 hours, until the chicken and vegetables are tender and cooked through.
Shred the chicken with two forks, and then return to the slow cooker. Taste and season the mixture with salt and pepper, if desired.
Chop each biscuit dough round into 8 bite-sized pieces. Place the biscuits in a large bowl or gallon-size Ziploc bag. Add the cornmeal and toss to coat the biscuits in the cornmeal.
With the slow cooker on the HIGH heat setting, drop the dumplings into the slow cooker. Cover and cook for about 1 more hour, until the dumplings are cooked through. They should be plump and doughy, but not raw. Don't stir the dumplings too much while they cook, or they may fall apart.
Ladle the chicken and dumplings into bowls and garnish with chopped fresh herbs.