I actually thought this might've been how it happened but, if you read Hashirama's bio:
" In the aftermath of intense battle, Hashirama defeated Madara, who faked his death and went into hiding, while Hashirama's wife, Mito Uzumaki, became the Nine-Tails' first jinchūriki by sealing the beast within herself. The devastation to the terrain which ensued from this battle were so great, that it created an entire land formation that would become known as the "Valley of the End" (終末の谷, Shūmatsu no Tani).
During his time as Hokage, Hashirama came into possession of a scroll filled with, among other skills, various kinjutsu, which he sealed away in order to keep the techniques within it a secret. He also defeated Kakuzu, who had been sent to assassinate him by Takigakure. At some point, Hashirama gained control of several tailed beasts. He spread these beasts to other, newly-formed villages in an attempt to maintain peace and equalise the powers between the nations. Thinking about the future of Konoha, he also trained the young Hiruzen Sarutobi, one of his brother's team members. He lived long enough to meet his first grandchild, Tsunade, and noted that he had spoiled her a great deal, even going as far as to teach her how to gamble. Hashirama died some time after the founding of Konoha in one of the many wars that were raging during this revolutionary era, but not before passing on the title of Hokage to Tobirama."
Straight from Narutopedia.
It seems like he accomplished a lot after Madara's "death", so your theory may be flawed.
