1. Soak wood chips in water 1 hour; drain well.
2. Trim excess fat from turkey. Loosen skin from breast by inserting fingers, gently pushing between skin and meat. Combine 2 teaspoons thyme, 1 1/2 teaspoons salt, pepper, and garlic, stirring well. Rub thyme mixture under loosened skin.
3. Heat oil in small saucepan over medium-high heat; swirl to coat. Add remaining 1 teaspoon thyme, remaining 1/2 teaspoon salt, and shallot; sauté for 2 minutes. Add juice and sugar. Bring to a boil; reduce heat, and simmer 15 minutes or until syrupy and reduced to about 1/2 cup. Remove from heat.
4. To prepare turkey for indirect grilling, remove grill rack. Preheat the grill to medium-high using both burners. After preheating, turn the left burner off (leave the right burner on). Place 1 cup wood chips on heat element on right side. Place a disposable aluminum foil pan on heat element on left (unheated) side. Pour 2 cups water in pan. Coat grill rack with cooking spray, and place on grill. Place the turkey on grill rack covering left burner. Cover and grill for 1 hour and 20 minutes or until a thermometer registers 165°, turning halfway during cooking time. Add the remaining 1 cup wood chips halfway during cooking time, and brush turkey with half of pomegranate mixture during last 5 minutes of cooking. Place the turkey on a platter. Let stand 30 minutes. Discard skin. Serve with remaining pomegranate mixture.