Once they are sworn, they are under the care of the military. Even medical and/or dental services performed while their on on leave (even if paid for by the cadet or parents) must be reported to the academy and placed in their medical file, to ensure their readiness for duty.
However, most people recommend that a new plebe/swab be kept on the parent's insurance for at least the summer, just in case of a severe injury or illness that may result in their disenrollment from the academy.
In such cases, the former cadet/midshipman may have trouble finding coverage for the condition or injury.