No, in a word, as SteamTrain says.
Quarterly Estimated taxes are paid with the 1040-ES. Unless you enter the 1040-ES into TurboTax separately, TurboTax would have no way of knowing what you had paid during the year. As SteamTrain notes, all other forms that report income and withholding (e.g., W-2, 1099s, and so on) include the taxes paid, so they don't need to be included with "estimated taxes paid".
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