No, they cannot. They can obviously encourage you to do so, but it is your choice whether to purchase health insurance, whom to put on your plan, and (if there is a choice of plans) which plan to buy. Even if you are under some court order (e.g. from a divorce, to provide health insurance for a child), the company cannot enforce that order against you (though a court could, of course). Private employers cannot add people to their employee's health plans.