My suspicion that they would destroy the sun has more to do with their action as potential heat sinks due to their indestructibility than their drain abilities.
Sorta ties into something I thought about much earlier;
-- The easiest way to prevent LV from killing HP would be for HP to convince LV that his intention is misguided. -- His intention is to kill Harry to save the world. (funny, that) -- Killing Harry will not save the world. It is clear that LV is aware of this, based on his reflections on self-fulfilling prophecies. -- LV intends to defy the prophecy at every point of intention, and will therefore try to kill HP anyway, because if the prophecy is coming true anyway he's already screwed and has nothing to...
And that not-aging thing the regeneration ability grants her isn't necessarily going to be awesome either. What if her body decides to continuously regenerate into the form of her present-aged self?
Exactly my thought. Aaaaand there was mention of apparating one into the sun.