Once your return is accepted, it should be processed and refunded within 21 days if you chose direct deposit as your refund method.
If you chose a paper check, you would add an estimated two weeks from the date of Approval.
TurboTax will not know anything about your mailed return, and will continue to show “Ready to Mail” on your account. TurboTax will not know that you put your tax return in an envelope and took it to a mailbox. TurboTax does not get updates on mailed returns. Wait about 4 weeks from when you mail a return and then you can check the status on the IRS site. https://www.irs.gov/refunds