Will Turbo Tax automatically add $10,200 to Box 4 of my 1099-G?

No, TurboTax will not add $10,200 to box 4 of your Form 1099-G. That's not how the unemployment exclusion works.

Form 1099-G box 4 is tax that was withheld from your unemployment benefits. But the $10,200 is not tax, it's a reduction of the amount of income that is subject to tax. Up to $10,200 of your unemployment benefits is excluded from your taxable income, so you don't pay any tax on up to $10,200 of unemployment benefits.

TurboTax will give you the exclusion automatically if you have unemployment income and your Adjusted Gross Income (AGI), excluding your unemployment, is less than $150,000. The exclusion will appear as a negative amount on Schedule 1 line 8 of your tax return.