I've done it with Captain Falcon - with 5 lives. This was before I was into competitive-ish stuff and when I still had the game for real, not emulated on my Wii (regret getting rid of it still...).
At separate times I've cleared the all the stages, including the fighting Polygon team and Metal Mario without losing stocks, as well as Master Hand (3 hearts during the Polygon team with my percent over 150 - timing so good XD ). So if you string it all together, yes, I've done this. But not all at once, no.
I've heard rumors that Isai has cleared the mode without taking any damage, although I highly suspect that was someone making a statement that is merely realistic based on his skill level (I don't imagine he plays 1P mode much).