Consider Mary, the super-scientist of Knowledge Argument fame. She has never seen red and yet knows everything there is to know about the physical nature of red and the brain processing related to color experience. Now, as a twist, suppose we show her red subliminally (say with backward masking or something). She sees a red fire hydrant and yet denies that she saw anything except the mask (say). Yet we can say that she is primed from this exposure (say quicker to identify a fire truck than a duck subsequently or something). Does she learn what it is like to see red from this? Does she know what it is like to see red and yet not know that she knows this?
It seems to me that views which accept phenomenological overflow, and allow that there is phenomenal consciousness in the absence of any kind of cognitive access, have to say that the subliminal exposure to red does let Mary learn what it is like for her to see red (without her knowing that she has learned this). But this seems very odd to me and thus seems to me that this is a kind of a priori consideration that suggests there is no overflow.
Of course I have had about 8 hours of sleep in the last week so maybe I am missing something?