No, TurboTax cannot tell if the IRS took your payment. The IRS does not share any information with TT after you file. TurboTax never knows how, when or even if you paid your tax due. Your proof that you paid will be your own bank or credit card statement or cancelled check.
You can check your online account with the IRS.
https://www.irs.gov/payments/your-online-account
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