Is this a viable world river system?

[Porklet]

I have tried to create a realistic river system for the world I am working on based on the information I got from the Sticky post "How to get you rivers in the right place" by Ryan K. I think I have done that, but I wondered if some more experienced map makers might take a look at my work. The map is 6,000 miles by 6,000 miles and is representative, at this point. The rivers shown are major river systems. I have included the 30th parallel in order to show the dry/arid zones and the wet zones to the north.

The area marked "A" is an experiment. I don't know if it can function this way. The south side of the mountain chain is in a rain shadow. The rivers flowing out of it are from the substantial snow melt cascading out of the valleys south. There are a few elevated mountain lakes, and the system then flows in to an expansive and very dry savannah. I intended for the map to show a varying flow river system collecting in a dry lake bed, filling, and evaporating seasonally (much like the African savannah without the torrential storms). I am wondering if that situation is realistic, and, if so, is it clear on as presented on the map?

Thanks for any help.