He would have died he left the tree.
Spiral Zetsu was most of the time attached to the Gedo Mazou. At that point Madara had Rinnegan, so if he used Spiral Zetsu as a suit; he could get enough of a boost to travel to Nagato's location; summon the Gedo Mazou, re-attach himself, Destroy the Uzumaki Village with the Gedo Mazou, (Does it fit in the timeline ? I will have to ask ISOKOROPS), trace Nagato, put him in Genjutsu and transplant his eyes.
You guys also seem to forget that Nagato was a cripple yet traveled from the Rain Village to Konoha just with Konan's help. Madara on the other hand had a whole troupe of White Zetsus to help him.
The hint that supports this is the Tobi Persona. It consisted of three identities : Spiral Zetsu, Obito and Madara. Tobi (Obito/Spiral) used Madara's name so I think it might hint that Madara used Spiral at one point. Plus Madara calls Obito his successor implying the transfer of Spiral Zetsu from Madara to Obito.
And for those who think Spiral was formed when Obito was brought into the Hideout; the answer is nope; Spiral was formed by Madara a few years after he summoned Gedo Mazou and Spiral was attached to the Gedo to re-supply his chakra.
Probably gave them to Zetsu who in turn transplanted them into Nagato. A better question is how Nagato and his parents didn't realize he had a pair of bright purple freakish eyes into his eyesockets.
Nice point ! In that case, I would assume Madara put his parents under Genjutsu as well and later staged their deaths by Konoha Ninjas to trigger Nagato's Rinnegan ?
Just throwing out ideas. :lol