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Cook sugar in a dry 1-quart heavy saucepan over moderate heat, undisturbed, until it begins to melt. Continue to cook, stirring occasionally with a fork, until sugar is melted into a deep golden caramel. Add 1/2 cup pomegranate juice (use caution; mixture will bubble and steam vigorously) and simmer over low heat, stirring occasionally, until caramel is dissolved. Remove syrup from heat.
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Pour pan juices through a fine-mesh sieve into a 1-quart glass measure or bowl, then skim off fat and reserve 1/4 cup of it. Add enough turkey stock to pan juices to total 31/2 cups liquid. Straddle roasting pan across 2 burners, then add water and deglaze pan by boiling over high heat, stirring and scraping up brown bits, 1 minute. Pour through fine-mesh sieve into glass measure with stock.
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Whisk together reserved fat and flour in a 3-quart heavy saucepan and cook roux over moderately low heat, whisking, until pale golden, 7 to 10 minutes. Add hot stock mixture in a stream, whisking constantly to prevent lumps. Bring to a boil, whisking, and add pomegranate syrup, then reduce heat and simmer, whisking occasionally, until thickened, about 5 minutes. Stir in any turkey juices accumulated on platter and simmer gravy 1 minute. Season with salt and pepper and stir in remaining tablespoon pomegranate juice.
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Remove string and skewer from turkey and discard onion and thyme from cavity. Serve turkey with gravy on the side.