In a voltage multiplier, must the frequency be low enough to allow for charging in first stage before switching?
Not quite.  For N multipliers there are N cap and N diodes or N pairs.  

The 1st pair and all odd pairs clamp the sine wave.
 The next (even pairs) rectify the AC-pp waveform and this repeats.
 The value of impedance of C is chosen to match the highest sine wave f available such that the cap impedance x N is small compared to the load R otherwise in addition to diode loss there is impedance loss. You choose the loss to be low to enable low ripple.