No. Turbo Tax sends notifications once your tax return is accepted or rejected. After it is accepted, it can take anywhere from a few days to 3 weeks for your return to go from acceptance to approval. If you are expecting a refund, you may check your refund status as well as your e-filing status by using the link below:
https://ttlc.intuit.com/questions/1908859-how-do-i-check-my-e-file-status