Yes- It might.
If you have the retirement plan checkbox on a W2, that impacts the entire year. You don't separate times of the year worked for this purpose, so your ability to make a deductible contribution will be based on both of you having retirement plans in 2016.
You can receive a full deduction if your MAGI is no more than $98,000.
https://www.irs.gov/retirement-plans/plan-participant-employee/2016-ira-contribution-and-deduction-l...
