Yes, all is fine. The accepted in TurboTax will remain that way from here on out. That is the status of your return; not your refund. That just lets you know the government received your return. Once the government accepts your return, they no longer provide any updates to TurboTax about your refund; so that status won't change.
If you now see a deposit date and are approved on Where's My Refund, that is the most accurate information and you are good to go!