No, because you filed your tax return close to the due date, the IRS has received an overwhelming number of tax returns to process.
Once your tax return has been e-filed, and accepted, TurboTax doesn't have any other information about your refund. If you are referring to your federal refund, you can check your federal refund status here.
For additional information, refer to the TurboTax article Where’s My Tax Refund? How to Check Your Refund Status for additional information.