TurboTax would not know when or if your stimulus check is deposited in your account, as that is confidential information only accessible by your bank and the IRS.
The e-mail went out to individuals who had their TurboTax fees deducted from their refund, as they are the tax filers who were likely affected by the issue. Consequently, you may not receive another e-mail when your deposit occurs.
Stimulus payments began to be deposited yesterday (January 8th) for millions of our customers affected by the IRS error. We expect most of these payments to be available today, but banks could take a few business days to process your payment.
You can use the following link to learn more:
https://blog.turbotax.intuit.com/tax-news/why-havent-i-received-my-second-stimulus-check-48743/?cid=soc_fb_o_news_20210106_1
If you do not receive it by the time you prepare your tax return this year, you can apply for the payment on your tax return and it will be included with your refund.