Yes. If I remember correctly, you will see your Adjusted Gross Income (Gross Income minus adjustments) go down by that amount. So your taxable income decreases. Let's just say for example that you're providing $500/month. Your taxable income will go down by $6000, your spouse's will increase by $6000 assuming they file correctly. (Of course, keep receipts of your payments to the ex-spouse in case they do not correctly claim the extra income and the IRS comes calling). Try it with and without, and you'll see the difference in AGI.
