Did turbo tax mail my completed return?

No.  TurboTax does not mail your return for you.   If you chose to file by mail then you have to print, sign and mail the return yourself.   It has to have YOUR signature in ink on the line that says "Sign here".

https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online/00/26258

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.

Federal and state returns must be in separate envelopes and they are mailed to different addresses.  Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.