Not necessarily. It means it was Received by the IRS, passed the initial checks (such as a correct SSN), and is now in the queue to be processed. The IRS can still adjust and/or offset it.
Tax Season Refund Frequently Asked Questions | Internal Revenue Service (irs.gov)
No. Accepted means you entered enough data for the IRS to allow your return into the system for processing.
https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved
If accepted, they try to process it within three weeks but it can be longer. if you have earned income credit or additional child tax credit, it will be at least the end of February before you see your refund, due to the PATH act that requires that they hold your refund longer.
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