Apparently no. I've watched several videos about damage buff exploits and nobody mentions this buff.
Moreover, Zelda wiki states:
Weapons have a set amount of durability and will break when this value reaches zero, dealing twice as much damage as they do so.
This is only present on melee weapons description, bows description only mentions the durability.
I can confirm, after testing on a black Moblin, that a brand new bow and a badly damaged one, both with a fully charged arrow, deal the same damage.
This probably is probably due to the fact that melee weapons actually break on contact with an enemy, bows don't because what hits the target is the arrow.