No. TurboTax does not have a copy of your W-2 or any other tax reporting document you may have been sent by another third party. The program only imports the information from your W-2. TurboTax does not and can not import your actual W-2 form.
W-2's come from your employer, and they have until Jan. 31 to issue it. Some employers allow you to import the W-2 through the software, but for security reasons you still need information from the actual W-2 to import it. You might need to phone, email and/or snail mail an old employer to make sure they know where to send your W-2.
https://ttlc.intuit.com/questions/2561916-how-can-i-get-a-copy-of-my-w-2
https://ttlc.intuit.com/questions/1934390-how-do-i-import-my-W-2
https://ttlc.intuit.com/questions/2588751-why-can-t-i-import-my-w-2
https://ttlc.intuit.com/questions/2938482-how-do-i-take-a-picture-of-my-w-2-in-turbotax-online
https://www.irs.gov/taxtopics/tc154
Other ways to get W-2’s:
Pay Social Security $86 per W-2:
You can get a wage and income transcript from the IRS: It will not show the actual W-2, 1099’s, etc, but will show the income information the IRS received. It will not, however, show your state information. It will only show the federal information.
https://www.irs.gov/individuals/get-transcript
https://turbotax.intuit.com/tax-tips/irs-tax-forms/what-is-a-w-2-form/L6VJbqWl5