Certainly plausible! First off little is known about WHY Mokuton drains chakra...also with some basic chemistry matter is neither crested nor destroyed, simply transferred...so where does that chakra go?! I doubt it just sits there in the wood! It is easily possible it absorbs the chakra, and allows it to flow into the caster!
Hashirama is a tad more then a bad match up! He has the natural talent to challenge Madara, naturally you chakra reserves, and the ability to absorb chakra.
The dragon Jutsu may simply be one of the most efficient ways to take chakra from large targets like Kurama or Perfect Susanoo!
Remember White Zetsu (a watered down Hashirama clone) could absorb chakra so why can't the real deal?!