Like others have said he lacks the DNA to produce the chakra in his brain like Sharingan needs to awaken.
However Rinnegan is different and is awakened by producing Hagaromos chakra which evolve the Rinnegan.
There is a chance that it will work and a chance that it wont. However, I have confidence that it would because in Kakashis case, he unlocked Perfect Susan'o despite not being of Uchiha lineage. All he needed was the other eye and six paths power.
Remnants of Hashiramas body tremendously boosts the power of doujutsu by relieving it of strain and cool down time.
If Hashi gets EMS I believe he will get Rinnegan in maybe a matter of years or even months.
Not only that, but his body may get a particular boost thats related to asura in some way.
If Oro brought a Hashi like this back to life it'd have to be at 30% power and Hiruzen would still wreck.