Yes, the total tax paid will be applied to your 2020 tax return and the income from the distribution can be spread out over 3 years to avoid having a high income.
But keep in mind that you might have to withhold some extra taxes from other sources in 2021 and 2022 because you have the added income in those years but no income tax withheld from the distribution for these years because the tax withheld on Form 1099-R only gets credited to 2020.
Also, if you pay the amount back in the next three years then you can get a refund on any taxes paid. Please see this from the IRS:
"If, for example, you receive a coronavirus-related distribution in 2020, you choose to include the distribution amount in income over a 3-year period (2020, 2021, and 2022), and you choose to repay the full amount to an eligible retirement plan in 2022, you may file amended federal income tax returns for 2020 and 2021 to claim a refund of the tax attributable to the amount of the distribution that you included in income for those years, and you will not be required to include any amount in income in 2022."
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