No. TurboTax has no way to track a stimulus payment.
Go to this IRS website for stimulus information - https://www.irs.gov/newsroom/treasury-and-irs-begin-delivering-second-round-of-economic-impact-payments-to-millions-of-americans
I suspect you will be able to check here beginning next week
https://www.irs.gov/coronavirus/get-my-payment