From my observations the Health bar in the Details screen has to do only with strength. When it's low enough, the label on the left changes to "Weakened." But if the label indicates the person is "sick" (and I just tried this with a proven makes-you-sick potion), the red bar is no shorter.

I don't know if repeated ingesting of bad potions would gradually affect the red bar, and I'm not willing to try it on anyone. But I do know that a very low bar yields weakness rather than sickness.

It does seem that the healing process should take a little longer - instant cures, even in this compacted time scheme, seem a bit unrealistic.

Disclaimer: I opted to play in Easy Mode, so some of my notes may not apply to the more difficult modes.