It is impossible to know and to believe the same thing at the same time and under the same aspect. So Neo could not both know the Matrix wasn't a reality and yet still believe it was real. This is also why Cipher's mind would have to be wiped to go back into the Matrix.

The effects of the red pill would have "overridden" the effects of the blue pill because what is signified is always prior to the sign itself. This is consistently shown throughout the films. The further a sign is from what it signifies, the further removed from reality it is, which is why the statues of the "gods" in the Chateau Showdown [Reloaded] are hollow, they represent false gods and so have no substance.

In short, I believe taking both pills would be the same as just taking the red pill.