With this in mind the most important part of drying a brush has got to be to shake as much water as possible out of the brush.
Short answer: Yes, it does make a difference, but only if you are selling brush holders. Otherwise, it does not make any difference at all. Long answer: Perhaps look at it this way: Shavers in times long past almost universally used shave brushes. Most of these gents did not have a brush hanger, and simply stood the brush on its end with the bristles pointing up. Amazingly enough, the brushes did not explode and did not even fall to pieces. Current production materials and methods are at likely at least as good as before, if not better.
Hint, spin your brush out if you don't have a rack to hang it. I shake and spin between my palms, much like when you want to dry a paint brush. I keep my brushes upside down and find they poof out better that way. Not once has water been left in any of my brushes. Once in a while you can even comb them out to hold their shape and keep them nice. Remember, hair goes on living even after what it was growing out of is dead. Give it a spin and upside down is no problem.
I've read it doesn't matter but I still hang mine to dry anyway because it's more convenient to store them this way for me. I have some cheap $5 plastic stands that I screwed into the wall inside the bathroom linen closet in the shelf area where I keep all of my shave gear. They are out of the way this way and it can't hurt to hang dry them anyway. Either way I wouldn't worry about it.
Let me rephrase that, you have to take care of it as when it was still attached to the living animal.
You could use one brush hanger for your brushes. The one that was used gets hung. Rotate the brush of the day to the hanger. The rest are dried and have no need to be hung.
Creepy, I just implemented this into my den yesterday. I usually put my brush in my room because it's more open an the air flows better than in the bathroom. But I noticed when I try my brush there is still moisture around the knot part =P so I took one of my stand and hung my brush in my room. The stand stays there now and the brush I use will be hung. I need to use my synthetic more often. =P my girlfriend got it for me, she thinks i don't like it because I have not used it for a while. I'm trying to break in my boar by using it exclusively =P