Yes, If all requirements are met. SIMPLE IRA contribution limits  are not cumulative with traditional and Roth IRA limits. However, SIMPLE IRA limits are cumulative with the contribution limits for other employer-sponsored plans, such as 401(k) plans and 403(b) plans. A simple plan is considered being covered by a retirement plan at work, so the traditional IRA may have limits on the deductibility on his 1040.