Turbo Tax does not say approved. It says Accepted or Rejected. If it was Accepted then the IRS got it and then processes it. Then the IRS Approves it. Yes It will go to your refund method.
If you used the Online version you can check your efile status here
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
When you efile you get back 2 emails. The first email only confirms the transmission. The second email says if the IRS (or state) Accepted or Rejected your efile. And check your spam folder for them.
When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. What does it say?
