Well, from what is shown, the Shinju is made of chakra too, or made out of chakra, as Momoshinki explained. So I guess absorbing the tree will lead Madara to gain more chakra and power, and evolve the Rinnesharingan and gain complete immortalitu.
The tree also seemed to be the part Kaguya was inside, since she talked to Madara in it or something.
So absorbing the God Tree would just further enhance him with more overall chakra? because besides completely healing him from the damage done to him by Guy and Naruto's Lava-enhanced rasenshuriken, there wasn't much evidence that absorbing the God Tree gave him a substantial power-up from what he already had shown
It seems that it completed his body to the lengths of immortality, equal to only Kaguya, as we see the guy who barely survived two almost situations, easily handle his body being sliced intp half.
Guess it was also the last piece to put for Kaguya to appear. It seemed she had her conscious and probably the key to her Rinnegen at there
Talking about that time, I'm still not impressed over Naruto letting Madara get powered up like that within that situation, instead of just ending him while he's injured and weaker, guess he badly wanted to team up with Sasuke to let it all go like that.