First of all I think this is a cool idea. I also definitely think it is possible although you may need to get another bit in order for it to trigger the Volca or Monotribe correctly.
Both the Volca and Monotribe have "sync" inputs and MIDI inputs so you can choose to trigger them using either method. The way you have it set up currently using the audio output of the synth speaker most likely will not work to trigger the synth, however, there are bits that are specifically designed to output the control voltage needed.
On the Volca/Monotribe the "sync" inputs are essentially control voltage inputs. Luckily LittleBits and Korg have collaborated and have created a control voltage bit here: control voltage bit. If you use this bit in place of the synth speaker, and connect the CV out to your Volca or Monotribe sync in, you will have the proper signal to trigger each step of your sequence.
Another method is to control the Volca or Monotribe using the MIDI bit here: MIDI Bit. I haven't yet experimented with how well the MIDI bit sends trigger messages out from the modules so may take some research to get it to work like you want it too.
My guess is that the CV module is going to work right out of the box, so for the sake of simplicity it would probably work best. Little bits also has the Synth Pro Pack that has 2 CV bits, MIDI, and a USB I/O: Synth Pro.
You also may want to think about how you trigger the roller switch. I know that it can be a little bouncy so depending on what you use to trigger the switch you might end up sending a bunch of triggers every time the reel turns rather than just one clean trigger. One way to avoid this would to make a cam of some sort so that the roller trigger is in contact with the reel the entire time and gently pushes it in as the long end of the cam comes around. On the other hand it might sound cool if a quick handful of triggers happen as the reel turns.
Anyway, I hope that helps. If you do build it I'm sure we would all love to see it submitted with video ;D