Sorry it doesn't. Turbo Tax will never know if or when you mailed it and the IRS doesn't update Turbo Tax when they get a mailed return. Turbo Tax will always say Ready to Mail or Printed.
4 weeks after you print and mail it, you can start checking IRS Where's my refund https://www.irs.gov/refunds/
Accepted or Reject is only for efiled returns.