Whether or not you are covered by a retirement plan at work for making a contribution to an IRA is not relevant if you do not have taxable compensation.
If you do not have taxable compensation you cannot contribute to any type of IRA.
IRS website for IRA contributions - https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-ira-contribution-li...
Go to this IRS website for Publication 590-A page 6 for compensation information - https://www.irs.gov/pub/irs-pdf/p590a.pdf#page=6
