Let's think logically. If the God Tree roots reach throughout the entire planet, then it's unlikely they suck chakra from humans, meaning humans didn't have chakra pre-Hagoromo, otherwise humanity would have ended the moment God Tree appeared on Earth.
That means whatever the God Tree sucked, couldn't have been chakra from humans, because there would be no humans to speak of by the time Kaguya arrived.
In that case, Amado probably meant chakra from the planet itself.... but can a planet have a chakra? Most likely not, in that case, Kodachi probably used the word chakra erroneously and meant to say sucks natural energy from the planet, which makes more sense and was even stated in the anime.
So in my humble opinion, this makes much more sense:
- God Tree sucks natural energy from the planet it's embedded in (stated in anime)
- Also feeds on human blood (stated in 4th databook Jin no Sho)
Also we were told the Jubi is nothing but natural energy by Kurama, but if the God Tree is its final form and produces a chakra fruit, said natural energy creature somehow produces chakra after sucking natural energy and blood, probably.