[Suicide Junkie]

Of course it dosen't.
It would really silly if completely destroyed armor were to regenerate.

As for specifics, the regen ability from any particular armor will fail at 50% damage (as seen in settings.txt)
Kwok also determined that if the armor is given time to regenerate back to 0% damage (thanks to other armors on the ship, or the hull's regen ability for example), then the ability will reactivate and contribute to the global regen rate again.