Rats can eat almost anything and thrive. They also eat grains. Quite possibly, if it were for the human farmers, rat's ancestors would have little chance to discover the flavour of grains. But they adjusted their digestive systems and metabolisms and probably do not get diabetes or heart disease, though sometimes they do look a but fat (by the way, the fructose-fed rat is an experimental model used in research on diabetes).
So, perhaps it is possible to adapt, after all. If indeed rat is well adapted to eating grains, it is worth observing that it reaches reproductive maturity at 3 months, and has 4-7 litters per year. Multiplied by an average litter size it would give about 50 offspring. Early Neolithic humans would have probably had one child every 2 years (it was about 4 years in Paleo times when children were breast for 4 years and infanticide was practiced). The difference in the potential for natural selection is hundredfold! So 10,000 years of evolution for humans was worth 1,000,000 for rats! One million years ago Homo sapiens, or even Neanderthal, was not around yet.
I guess we can be optimistic, give it another 990,000 years and will be well adapted to eating grains.