You are quite exaggerating, but Asa kujaku might indeed cause a lot of fiery damage to ss, since wood is prone to fire..
Not really tho. Hashirama's (lets call it "regular") mokuton get negged by asakujaku as we've already seen how Madara burned his own mokuton with Katon, so fire works against mokuton. Not only Asakujaku is fire, but it's also taijutsu, which can break the wood on it's own (And with many hits, it can take down the many branches it generates).
When things get serious with Shinsuusenju, since it's still wood , fire should work as well, but Hirudora, as it took down Madara's Susano'o, should be able to destroy part, if not all, of the wood construct as well in the explosion.
Gai may have his work cut out in 7th gate, but I guess with high diff he can take Hashirama down. 8th gate is out of the question.