Very basic resistor/piezo question

With the resistor in parallel, you are creating a voltage divider where one of the "resistors" is the internal resistance of the piezo device. Yes, that will reduce the voltage. Since the piezo (unlike most voltage sources) has high source-impedance, a high-value resistor in parallel will reduce the voltage.

Piezo elements are perhaps more accurately though of as capacitors with a current source built in -
mechanical strain directly moves charges around in the material. They have very high DC
resistance (the value of which isn't really useful - their capacitance is more interesting). Adding
a parallel resistor creates a high-pass filter which eliminates DC offset and drift and creates
a signal that more represents velocity than displacement of the sensor - often more useful.