Yes, you will still get your Stimulus Payment if the IRS accepted your 2019 tax return. It doesn't matter if the State accepted your tax return or not in order to receive your Stimulus Payment.
@ReginaM Do you know how long it takes the IRS to process a Tax Return? I used the "TurboTax free
Stimulus Registration for non-tax filers" which automatically e-filed a 2019 Tax Return to the IRS on April 4th. Right now I checked the status of the return and it said that the IRS received it, but hasn't approved it yet. I'm guessing that they have to approve it before they have your info and give you the stimulus check and I was wondering how long does that take? If enter all of my information on the Get My Payment tool on the IRS website I get an error message saying "Payment Status is not Available, According to the information that we have on file, we cannot determine your eligibility for a payment at this time."
Select https://www.irs.gov/coronavirus/economic-impact-payments and select the get my payment option to review your stimulus payment status.