I'm not clear that you understand that *YOU* have to print sign and mail your returns. But you do. TurboTax will not mail anything for anyone under any circumstance. But when you select the print and mail option, the TurboTax program will show "ready to mail" forever. TurboTax has no way of knowing that you actually mailed them. The "Ready to Mail" status will be there *forever*.
If you forgot to attach a document to your tax return, then you should ***WAIT*** for the IRS to send you a letter specifically requesting you to send them a copy of your W-2. They may or may not request it. So just wait. If they want your copy (as opposed to the copy your employer sent them) then the IRS will specifically ask you for it.