Had Lews Therin balefired himself his soul would have been ripped from the Pattern and Rand could not have been born, if I understand the lore correctly.
On a non-canon point, it would an interesting idea, death by self balefire. As this would remove you from the pattern in the past... Meaning you would not have balefired yourself. Would this create a temporal paradox like killing your own grandparents in the past? Or in the case cited, would LTT and his soul be removed from the Pattern and Ilyena and the others be restored to life? Could he have undone the attack on Shayol Ghul? I guess undoing something like that would destroy the Pattern quicker than destroying whole cities as the Age Lace is woven around such important events.
To be fair, I think Jordan kept his magic system soft to avoid such paradoxes. I feel Sanderson would be the kind of author to explore the implications this would cause in a hard magic system, like he did with Gateways in his books.