I believe that you may have misheard the statement: "He will do it of his own accord", which means he would do it without any prompting from others.
See: of own accord - Idioms - by the Free Dictionary, Thesaurus and Encyclopedia.
"of one's own accord and of one's own free will
by one's own choice, without coercion:
I wish that Sally would choose to do it of her own accord. I'll have to order her to do it because she won't do it of her own free will."
That was my first instinct too though I did wonder if perhaps it was "go", not "do" but that would be a less likely mishearing given the difference in the pronunciation of the two words.