No. Although your W-2 will show FICA (social security and medicare) taxes paid, and will be entered in TurboTax (TT), that information will not be entered anywhere on the actual tax forms.
There is one case when TT will use the W-2 info: if you also need to report self employment income, TT will see to it that you are not over taxed if your total income is over the SS max.