What does unearned income have to do with it?
The EIC is based on the earned income or the gross income, whichever gets you a smaller EIC.
A contribution to a traditional IRA will only reduce your gross income not your earned income.
i.e. If your only income is 50k on a W2 it wont help if your gross income is reduced. However if your income is 40k W2 and 10K i.e. rental income (=50k gross), and you contributed 10k (6k self + 4k spouse) to a traditional IRA, your EIC will be based on 40k instead of 50k.