No. "Accepted" and "approved" do not mean the same thing. "Accepted" only means you entered enough data for the IRS to take your return and start processing it. Approval is a later step.
https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved
Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 34of your 2020 Form 1040) of your federal refund to track your Federal refund:
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others
If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
https://ttlc.intuit.com/questions/3397970-path-act-delayed-refunds-for-some-filers
So once it is approved that would mean I am receiving the refund? If it was not for some reason would it also inform me with that notice? @xmasbaby0