My employer offers a plan with very limited benefits. It only covers preventive services and a few doctor visits each year. However, this plan option is free. If I sign up for it, will that satisfy the individual mandate to have coverage?

Yes, most group health plans offered by an employer are considered “minimum essential coverage.” Some limited benefit plans (for example, dental only plans) are not considered minimum essential coverage.  Your group health plan materials should indicate whether the plan is considered “minimum essential coverage.”  If it is and if you enroll in the plan, you will have met the requirement to have coverage and won’t owe a tax penalty.  However, the plan you described probably does not meet the standard for “minimum value.”  If this is the only plan your employer offers, you may be able to qualify for premium tax credits to help pay for Marketplace coverage.  The premium tax credits could help you afford coverage that would be more comprehensive.