Hello again, @billberman5 !

That will depend on your total income, and whether you have paid enough taxes in withholding and estimates to cover your total tax liability for the year. 

For 2021, there has been no word that the law change that made a portion of everyone's unemployment compensation non-taxable will be extended. I would not count on it! So, the income will count the same as wages. 

Is there a AGI threshold at which there is no refund for any unemployment taxes?

No.  It depends on your total income and withholding from all sources for the year.   If your total income is less than the Standard Deduction you will get all your withholding back.

For 2021 the standard deduction amounts are:

Single 12,550 + 1,700 for 65 and over or blind (14,250)

HOH 18,800 + 1,700 for 65 and over or blind

Joint 25,100 + 1,350 for each 65 and over or blind

Married filing Separate 12,550 + 1,350 for 65 and over or blind

So..lf my total income is far greater than a married, standard deduction, at this point in time, I should not expect a refund of any sort on unemployment taxes?

You might get some back if your total withholding is more than the tax on your income.   It is not broken out by kind of income.      all your income and withholding are lumped together.