i think so. it's yet unclear how madara died, but since tobi's story of madara loosing the fight at will, surviving and getting the senju-dna to explain why he is still alive is obviously wrong, i currently think that madara died in his final fight against hashirama.
i dont know why you consider it being impossible for hashi to beat rinnegan+ems-madara, since we know like nothing about hashi at all. we have never seen hashi in a real fight, so there's no possibility to decide what he can do with his mokuton, how fast he is and what additional jutsus he can use.
based on the general story that was believed in the narutoverse, that hashi killed madara, i think it's safe to assume that if madara had the sage's eyes, his concurrent hashirama would have the sage's body, which basically should be as strong as the rinnegan, whatever it may be.
about his knowledge about nagato: no idea where he nows him from. but if hashi didnt kill madara, who did?
Well first off about his speed. Oro's IWR was weaker than kabuto's but only because Oro was controlling them so they didn't have the full range of their arsenal. The speed and strength we saw in the fight against Hiruzen is the speed and strength that Hashirama has to have. He can't have more, unless you think that all the IWR's created by Kabuto are actually much faster and stronger physically then they have been shown to be.
Secondly the rinnegan is pretty much the most OP thing ever, followed closely by the EMS and the abilities that even a normal sharingan gives you. Because of this taijutsu would be useless against someone of Madara's speed because of the benefits of a 3 tomoe sharingan. And he could copy any jutsu that Hashi uses with the sharingan and because of the rinnegan he can use all jutsus that aren't KG. (maybe KG it hasn't been proven either way but I am being safe)
So since taijutsu is a no go, and genjutsu would be stupid since Madara has two things that can see chakra and see through some genjutsu, that also would be fairly useless. Now let's go to ninjutsu, Madara can absorb literally everything that Hashi would throw at him. He can take hashi's attacks and use it to gain more chakra. OP maybe? And he doesn't even need to do that, he could use shinra tensei to knock everything back, or to pull in Hashi and kill him like Nagato did to Fukasaku.
And that isn't even all of the abilities that Madara has, he has Susanoo, at least two more EMS powers, his inferno fireball jutsu, is skilled with a blade, and is extremely fast.
So combining someone who is already top level without the with the rinnegan just makes them super OP. Did you see how many people he killed before he even had the EMS activated? And he didn't even attack with EMS, he only defended himself.
P.S. To that kid who posted a picture of that fight and said Madara looks scared or angry. Look at Madara's eyes, do you see the rinnegan? Doesn't look that way to me. Hashi couldn't do it.