No. Reporting your HSA will require Form 1040 which is NOT included in the free version.
You will need Deluxe.Click on FORMS to see what's included.<a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/personal-taxes/online/free-edition.jsp">https://turbotax.intuit.com/personal-taxes/online/free-edition.jsp</a>