digital rheostat pot - not closing entirely?

Will this work with turning volume up/down?

Basically yes but there are two problems:-

  1. It is a linear pot, not a log one. You normally use log pots for volume control because the ear's response is log ( or close to log ). By using a linear pot you will perceive all the volume change at one end.
  2. Because you have to have a pull up resistor the maximum output will only be half the input. That is if you make the pull up resistor the same value as the rheostat value.