Can I substitute a mono potentiometer for a stereo one?
Based on how I'm visualizing it (below), it seems like I should be
  able to. Am I missing anything conceptually?


Perhaps you're visualizing that the pots merely affect the control voltages fed to voltage controlled attenuators, one for each channel.

However, it is most likely that the pots actually form two separate voltage dividers feed by the analog signals for each channel.



If you combine the L and R signals in a single pot, you will no longer have separate L and R signals; each channel will carry a L + R signal.

As Kaz points out, it is also possible that you might damage the stages feeding the volume control.