No, you can't get your 2016, 2017 and 2018 W-2's from TurboTax. However, you may be able to get 2016 and 2017 W-2's from the IRS by getting an online wage and income transcript.

• Wage and Income Transcript. It shows data from information returns we receive such as Forms W-2, 1099, 1098 and Form 5498, IRA Contribution Information. 
• Note: 2018 tax information may not be complete until July. 
• See How do I get a copy of my tax return or transcript from the IRS?
• 2016 and 2017 income tax returns can't be e-filed. You'll have to mail them in. To prepare your 2016 and 2017 income tax returns, see Find out how.
  
• See also, Can I file a 2018 return if I haven't filed my 2017 return yet?

Additional information: Is it still possible to e-file 2017, 2016, or earlier tax returns in TurboTax?