Arduino Nano - A6/A7 internal pull-up resistors

dadaumpa:
Regarding pinMode(), that's curious. You mean it has no effect on A6/A7 because of their analog, input-only nature?

pinMode() has no effect on analog inputs (A0-A7).

When analogRead() is called, the pin switches to an analog input regardless of what the pinMode was set as.

dadaumpa:
Because the page http://arduino.cc/en/Tutorial/AnalogInputPins actually uses pinMode() on an analog pin.

Yes, because the code in that example is showing how to use the analog pin into a digital pin.