Yes, depending on which notification preferences you selected, TurboTax will notify you of the status of your return(s). If you would like to track your e-file status or any refund you may have, I included below, the links necessary to do so:
To check your e-file status, please click on the following link: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
To track your Federal or State refund please click on the following link: https://turbotax.intuit.com/tax-tools/wheres-my-refund/
You can also track your federal refund on the IRS website by clicking on the following link: https://www.irs.gov/refunds