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
It can take up to 4 weeks to process a mailed in return. The IRS recommends not even tracking it until that amount of time has passed. Please see the link here to track: https://www.irs.gov/refunds
You can also order a transcript here to obtain additional information as well: https://www.irs.gov/individuals/tax-return-transcript-types-and-ways-to-order-them