Does turbotax calculate the incorrect tax withheld?

No, TurboTax picks up the amounts you enter as withholdings in your return.

It only uses your input to report the amount of tax payments for federal and state.  

As the other poster mentioned in their reply, you manually enter or import the actual payroll taxes withheld as you enter the data from the relevant form. Turbotax does check the tax rate for some taxes (medicare, social security) and will alert you if the withholding you reported is incorrect.