(emphasis mine)Apologies, I misphrased my statement. It should have been more specifically stated as the unarmed strike not indisputably qualifying as a natural attack by RAW for the effects of the INA feat.
So...by your own admission, the result of taking INA is an effect, therefore a Monk can take INA to improve his Unarmed Strikes, RAW.
We could do this all day, but we should probably fork this to a new thread...which, like all of the other threads about this will go on for a while before being closed, all without resolving the issue...
because WotC designers were imprecise with language.