Out of curiosity, can someone who does not have a grain of rationality in them ever become more rational?

They may stumble across rationality as life causes their core functions to randomly vary. As far as I can tell, that's how explicit and self-referential standards of thought first arose - they seem to have occurred in societies where there were many different ideas and claims being made about everything, and people needed a way to sift through the rich bed of assertions.

So complex and mutually-incompatible cultural fluxes seem to not only be necessary to produce the first correct standards, but encourage them to be developed as well. That argument applies more to societies than individuals, but I think a similar one holds there too.

Short answer: only by chance, I think.