No, they do not. After age 65, the federal government picks up the hospital tab via Medicare, and depending on how many qualified assets you have, Medicaid helps with the rest.
Before 65, health insurance can only use a few factors to determine premiums, but none are related to one's health.
https://www.healthcare.gov/how-plans-set-your-premiums/
>Factors that can’t affect premiums
>They also can’t take your current health or medical history into account. All health plans must cover treatment for pre-existing conditions from the day coverage starts.