Yes, IRS might catch it but you won't hear about it until a year or so after the return was filed. You are better off to file amended federal and state returns after the original returns have been processed.
You should not amend a return until IRS has had time to process the original return fully anyway. Once that happens, then the 1040X will probably be available in TurboTax and you can reload your return and amend the federal and state returns at the same time.
The expected availability date of the 2020 Form 1040X in TurboTax is currently March 25, 2021.
The bad part is that IRS will have your balance due payment from your account when they process the original return, but the good part is that once you have filed your amended returns, then you should get the excess refunded.
