No. Not true unless you actually e-filed the tax returns in the File section of the program by clicking on the Transmit Returns Now button. Use this TurboTax website to check the status of an e-filed return and if it was either accepted, rejected on nothing found - https://turbotax.intuit.com/tax-tools/efile-status-lookup/
If nothing was found using the TurboTax website, then your tax returns were Not sent to the IRS and the website is incorrect. You can go ahead and mail your tax returns as you planned to do.
