If Hashirama has an advanged version of Tsunade's healing, I dont see him losing in any case though. And hashirama's heart would probably reject and kill him because his body wouldn't be strong enough to support a Senju heart. (probably the case)
What makes you even consider that?! Kakuzu's Earth Grudge Fear has no limitations in such a degree. He'd simply be able to take a heart and have access to its chakra. It wouldn't give him Mokuton, but it would provide him with his vast level of chakra pending how much focuses around the heart.
OT:
Kakuzu was an elite shinobi of Takigakure. He grew up in the same relative time period as Hashirama, Tobirama, and Madara. He was given a mission to assassinate Hashirama Senju, but during the conflict, he failed; however, escaped from being killed. Upon returning to the village, instead of being praised for doing his best, he was berated, ridiculed, and tortured for failure.
Unable to cope with the sense of betrayal and anger at his dishonor, Kakuzu lost hope in Humanity and gave up on his allegiance to Takigakure. He fled the village taking the secrets of Jiongou (Earth Grudge Fear), took the hearts of the village elders, and became a rogue. Other than this, we know he's killed several of his Akatsuki partners. He's paired with Hidan because of the latter's inability to well... Die.
