Put chicken, leek, garlic, broth, chicken salt, and pepper in 4-quart slow cooker. Cover; cook on low 6 hours until tender and at least 165°F.
Plate chicken; shred into large pieces. Add cream and cream cheese to hot liquid; cover and cook on high 15 minutes, stirring once until smooth.
Meanwhile, cook rotini with tablespoon salt until just tender. Reserve 1 cup pasta water; drain.
Turn cooker off; gradually add Parmesan. Fold in chicken and pasta.
Loosen with reserved water a few tablespoons at a time only if needed. Serve promptly while sauce coats rotini.