Yes, the distribution would add to your taxable income. The exception you take to the 10% early distribution penalty does not make the entire distribution nontaxable, it simply means you don't pay the early distribution penalty.
The distribution amount adds to both your Adjusted Gross Income and your taxable income. Tax is calculated based on your total taxable income. Then, all your tax withheld from ALL sources is added together and subtracted from the calculated tax due.
Because this income is added to your adjusted gross Income, it can change many hings on your return, other than just the tax due on this one amount. Credits that change according to your AGI can change,and so can your overall tax rate.
