Cook bacon in a large skillet over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Transfer bacon slices to a paper towel-lined plate. Drain and discard excess grease.

Crumble 4 slices of bacon into the same skillet. Add onion, celery, garlic, and thyme; cook and stir over medium heat until vegetables are soft, about 5 minutes. Transfer mixture to a large pot. Add corn and chicken broth; bring to a boil. Cook soup until flavors combine, about 5 minutes.

Pour 2 cups of soup into a blender. Cover and hold the lid down; purée until smooth. Return puréed soup to the pot. Stir in half-and-half, salt, and pepper; bring to a boil. Stir in shrimp; cook until shrimp are opaque, 3 to 4 minutes.