Yes, TurboTax notifies you when the IRS has accepted your tax return. Accepted is the first step in the process of your tax return processing. For more on the timing of your refund please see this TurboTax FAQ.
Check on Where’s My Refund? it has the most up to date information available about your refund. The tool is updated daily (usually overnight) so you will just usually need to check once a day.
**Mark the post that answers your question by clicking on "Mark as Best Answer"
That IRS "Where's My Refund" tool can be squirrelly at times. I'll give you some tips on using the IRS WMR tool lower down.
The IRS says 9 out of 10 filers who efile and choose direct deposit will get their Federal refunds within 21 days after being accepted. Some returns are processed fairly quickly, while others require additional processing due to specific items in the return. Some are pulled at random for more thorough investigation.
If you efiled, double-check to be sure the return was efiled successfully and accepted.
If you used Online TurboTax, you can sign into your Online Account and check the efile status at the Tax Home.
If that showed it was accepted, you can use the "Where's My Refund" tool at the IRS website below to monitor the status of your Federal refund.
NOTE: When using that tool, use only the Federal refund amount, and not any total refund amount that includes a state refund.
The amount to use is on your Federal Form 1040, Line 21a.
Also be sure the SSN and filing status are correct.
You can also try phoning the IRS refund hotline. I've seen it work for some users before when the WMR tool didn't.
To track a state refund:
From time to time as the return moves thru processing your return may not show on the IRS website especially now while the IRS is short handed and overworked getting out stimulus payments.