It does. The health drain Stamina incurs is relative to the regen of the character you're using... I installed Bob's Classes to test it and everything seems to work just fine.
Bob's Classes defines the new characters in the data phase.
Stamina performs its adjustments (mostly, tweaking regen and the "out of combat" delay) in the data-updates phase on all currently defined player types in such a way to ensure they all get penalized at the same rate (due to high vanilla regen, Stamina almost always decreases regen from the data phase so the craft capacity won't be tiny). Bob's Classes doesn't do anything to health or regen here.
Neither touches regen or health in the data-final-fixes phase.
Stamina's actual health drain is calculated and performed at runtime based on whatever the final definition ended up with. Are you using some other mod that does something to at runtime? Or a mod that might cause Stamina to think you're crafting, mining, or moving when you aren't (though if you left the mining/running penalties at their 50% default this shouldn't matter)?