No, you do not have to enroll in the student health plan. Eligibility for a student health plan does not make you ineligible for Marketplace coverage and subsidies. In addition, if you meet other requirements, you may qualify for premium tax credits to help you pay for coverage. Subsidies are calculated based on the price of available plans and household income; lower income individuals are eligible for greater subsidy amounts, and some higher income individuals may not receive subsidies. If your income is between 100 percent and 250 percent of the federal poverty level, you may also qualify for cost-sharing reductions.
In addition, eligibility for a student health plan does not make you ineligible for Medicaid. Check with your state to find out if you meet the income and other eligibility standards to enroll in Medicaid coverage. (26 U.S.C. § 36B; 42 U.S.C. § 18071)