Do Shimano MTB shoes in half-sizes make a perceptible comfort difference?
Simple maths will show that for 50% of the population, a half-size will be closer to their “true” foot size than an integer size. 

But the same maths will mean it won’t make a difference for the other 50% of the population. 

We can’t tell which half of the population you’re in and whether you’d benefit. 

P.s.  this assumes that the sizes of human feet are a continuous rather than discrete range. This is not a trivial assumption as long-term wearing of discrete (integer) shoes may deform half-size-feet into a shape closer to integers. It also assumes the same foot size on both feet which is definitely a dangerous assumption. 



Version 2 of my answer. 

If we want to assume different size left and right feet we have to do more stats. 

So ... assuming you have different size feet, that the shoes have to be bought in the same size, and that half sizes are available, I think the statistics would be 1- (50%*50%) = a 75% likelihood that one or both feet will be closer to a better fit when you have half sizes. 

This is compared to only a 50% likelihood when using integer sizes. 

There’s lots of false assumptions in v2 but the simplification (most notably the difference is size between two feet is assumed to be random) would lead to a lower likelihood and thus its likely that the actual improvement is greater than +25%.