Yes and no - water on a flat surface with an open edge doesn't drain at the same speed as water on a smooth slope. You can build up a shallow pool on each ledge that will spilling over the open side. With enough rain, the effect will be overcome and it will basically end up the same and with light enough rain, some of the water will get trapped on the roof and evaporate off but in the middle it should work.
I don't really feel like digging out my old fluid dynamics notes to try to calculate it out but the basic principle makes sense