No it does not."Bad health" means the character was pruned by the new system introduced in Reaper's Due.
The game is not set up to give a thousand reasons for death, just a handful. Bad health just means one of the other many things.The problem is he didn't die of any of those things. He died of "low health".
It is given to pruned characters, but not only pruned characters as your previous post suggested.Bad health is 100% the reason given for pruned characters.
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Also, please link to the Wikipedia page about sudden death due to being too unimportant.
Also pruning absolutely does affect the PC, I've seen tons of my own courtiers get pruned.