I don’t believe it would be a wash.
Example: Assume you make $100k annually. You reduce your withholding by $5k, so you bring home $5k more (your income doesn’t change because of this reduction in withholding). Use the $5k to fund a traditional IRA (which will drop your taxable income by a like amount). Assume you are in the 25% tax bracket.
Funding the traditional IRA will drop your taxable income from $100k to $95k, so your tax savings are $1,250 (.25 x $5k). However, your withholding on your W-2 dropped $5k. So your net tax situation has you paying $3,750 more ($5k less $1,250), which you’ll need to fund from somewhere.
Funding your IRA drops your income and saves you 25% of the amount in taxes. Dropping your withholding to fund the IRA drops your tax paid during the year, thus having a “dollar-for-dollar” impact on your tax refund or amount due.
Of course, I made a bunch of assumptions that may not be correct for your specific situation, but I would not consider it to be a wash (although it still may be worth doing!).