Said another way, eligibility to contribute to a traditional IRA only depends on age and having compensation to support the contribution. Eligibility to contribute to a traditional IRA does not depend in any way on workplace retirement plan coverage. It's the ability to deduct that contribution that depends on workplace retirement plan coverage.
If the employer has a defined benefit plan and the employee meets the eligibility requirements for participation in the plan the employee is covered even if the employee never vests or is eligible to collect benefits under that plan. However, it's unlikely that having only one day of employment would meet the eligibility requirements.
