TurboTax does not process your tax return. The IRS and state process your tax returns. TurboTax only provided the do-it-yourself software you used to prepare and file the return. After you file, the IRS or state do not provide any information to TurboTax. Your online account will only show that the result of the return you filed was "accepted."
The tax return status on the TurboTax Tax Home web page will remain at Accepted since TurboTax receives no further information concerning the tax return or the tax refund once the tax return has been Accepted by the IRS or a State.