Do I get an email from turbo tax verifying my taxes were e filed? If so how long does it take?

You should receive an e-mail within 48 hours whether the return was accepted or rejected.  Sometimes your return is in pending status and it can take longer.

Pending means that your e-filed return is on its way and that the government hasn't accepted or rejected it yet.

If you e-filed your return before the IRS starts processing returns this year, it'll stay in pending status until then. After that, e-filed returns generally sit in pending status for 24–48 hours before being either accepted or rejected. 

Even if you filed your federal and state returns at the same time, your state may not start processing it at the same time as the IRS. Your state return may remain in pending status several days after your federal return has been accepted.

After submitting your return in TurboTax, we may do an extra review of your return to make sure it doesn’t get rejected. When this happens, your tax return is pending. You should receive an email from us within 48 hours confirming that your return has been filed, or with instructions for any additional steps.