It will reduce, but perhaps not eliminate tax underpayment for tax quarters 1 through 3 even though you end up with a zero balance due. Try it and see.
The US tax system is pay as you go and whether or not you have an underpayment is evaluated on a quarterly basis. Because income is treated by default as having been received evenly throughout the year, a deductible IRA contribution will reduce each quarter's income by 1/4 of the deductible amount. That might not be enough to totally eliminate the underpayment for the earlier tax quarters, but it will at least reduce it.
