I have always heard that this was a no no, just like drying your brush upside down. Ive often heard the undesired results termed as "knot rot".
I do dry my brushes upside down because I never had a brush good enough to warrant a stand (although I did just order one). I just fill up my mug with water to get th soap nice and wet and soak my brush for a minute at most. Even with my cheap plastic brushes, I dont let the handle get wet if I can help it.