However, the properties of a mole of Nitrogen atoms in a jar has extremely PREDICTABLE properties.
So it is not inconceivable that a LARGE number of organisms undergoing RANDOM changes may have PREDICTABLE traits at the end of a long period. Mutations that cause DEATH will be quickly weeded out of the population, for one thing. Mutations that do not support survival would go away after a short time as well.
Diversity would occur from DIFFERENT mutations that INCREASE survival chances, maybe there would be a lot of these, maybe there are only a few. This is where the real question lies.