The 1M resistor would be in parallel with the piezo.
Regarding a "floating" input, if you were to stick a wire into any random analog port and try analogRead() on it you'll get somewhat random values. There is no pull up or down so radio waves, noise from mains circuits, static electricity, touching it... anything can affect the reading. That would be a floating input and I think that's basically what you have when there's no resistor in parallel with the piezo.
Tapping the piezo should generate a voltage that can be read by the Arduino but only for a brief amount of time. Pushing on the piezo or holding it pressed shouldn't cause much of any reading.