Mix drained canned beans, fully cooked sausage, onion, bell pepper, celery, garlic, paprika, thyme, cayenne, salt, and pepper in labeled gallon freezer bag. Remove excess air; seal.
Before slow cooking, freeze flat on tray up to 2 months. Keep broth and rice separate until cooking day.
Thaw sealed bag in refrigerator 24 hours. Empty into 6-quart slow cooker; add broth.
Cover; cook on low about 6 hours until vegetables tender and mixture hot throughout. Mash about 1 cup beans against side; stir in and cook covered on high 15 minutes.
During final 30 minutes, boil rice and 2 1/2 cups water in covered saucepan. Reduce to low; cook 15 minutes, then rest covered 10 minutes.
Divide rice and thickened beans among 6 bowls, distributing sausage evenly.
Refrigerate leftovers in shallow containers within 2 hours. Microwave covered, stirring midway, until beans, sausage, and rice reach 165°F.