I don't think Pokéblocks have an effect on the nature of the baby, but I do believe that in some way, the parents' natures have an effect.
I don't know for sure, but one time when I was trying to breed up a Beauty-loving Castform for one of the contests, I always ended up with one of a certain set of personalities, and nothing more. I only got a proper nature (it was Quiet) when I switched the father out for another with a different nature.
But I don't have any hard evidence for this, so don't quote me on this.