I mailed my taxes will TurboTax update when they reach IRS?

TurboTax receives no information from the IRS when a tax return is mailed.

No.  The IRS doesn't update Turbo Tax when they get your return.  Turbo Tax will never know if or when you mailed a return.  And mailed returns don't get Accepted or Rejected.  That's only for efiled returns.