Sorry no, once  your return has been accepted or you mailed it in, TurboTax does not get any more information about your return or refund.

 

Also, no one on this forum would know when you will receive your refund.  The IRS states that most taxpayers will receive their refund within 21 days (business days) of when their return was accepted, as long as you have e-filed, choose direct deposit, & there is no errors in your return.  States differ when they issue refunds.

 

Once your return(s) get accepted, you can check the status of your Federal refund on the IRS website,  Where's My Refund, updates only once a day.

https://www.irs.gov/refund 

 

Also, see the following:

 

• February 22. Projected date for the IRS.gov Where's My Refund tool being updated for those claiming EITC and ACTC, also referred to as PATH Act returns.
   
• First week of March. Tax refunds begin reaching those claiming EITC and ACTC (PATH Act returns) for those who file electronically with direct deposit and there are no issues with their tax returns.

 

If you have a state refund, see the following:

 

How do I track my state refund?

https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571