No, TurboTax does not and cannot obtain your W-2 for you.
Your employer has until 02/01/2021 to provide the 2020 W-2.
See this TurboTax support FAQ for importing a W-2 - https://ttlc.intuit.com/community/entering-importing/help/how-do-i-import-or-enter-my-w-2/01/26253
(You will need a copy of the W-2 in hand before the W-2 can be imported)
