Timing of the retard

I've wondered about this for a while: are there differences in the final product depending on when the retard occurs? 

I often include the retard as part of my bulk fermentation just because it's more conducive to my lifestyle--my fridge is usually packed on the weekends, which is when I'm baking, and being able to retard in my fridge in a container vs. a freeform loaf on parchment, improves the odds that the dough doesn't land on the floor or have a carton of OJ dropped on it (it's those 3 teens and the distracted husband that I fear).  I can also pace my days a bit better--knead and bulk ferment one day, shape and bake the next.

But in the quest for ultimate SD perfection, I wonder: does it make a difference?