Is qNaN easier than trapping on overflow?
It isn't the arithmetic that slows things down, it's the exception processing -- especially the processing required to clean up after an imprecise trap. qNaN defers exceptions, keeping the pipeline full for a greater percentage of the time.

There's no inherent reason that processing NaNs should be any slower than normal numbers, because the rules are quite clear. In fact, if anything, I would expect them to be faster.