Yes, the entire amount is taxable income in the year of the conversion.
The estimated payment is due September 15, for a conversion in August.
Also, when you prepare your tax return, you may see a penalty calculation anyway. The IRS assumes all income is spread out evenly over the year, so they expect taxes to also be paid evenly. That means that for a $100,000 Roth conversion taxed at (let's assume) 24%, the IRS will want to see payments of $6000 each paid on April 15, June 15, Sept 15 and January 15. To avoid a penalty for not making the earlier payments, you can use the "Annualized income installment method" which divides the year into 4 quarters, allocates the income accordingly, and calculates the tax due each quarter. By showing the IRS that your income was unevenly received, and you paid the right amount of tax for each quarter (via a combination of payments and withholding), you will not be assessed a penalty. Turbotax includes this calculation under "special circumstances."
https://www.irs.gov/payments/underpayment-of-estimated-tax-by-individuals-penalty
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