It really depends on the medium, but I think that in the media that do display them, they are just aesthetic.

If I twisted the inner workings of your back, I bet your arms would move too.

As a Bonkle myself I can confirm that it is possible to move other Bonkles' arms.

If I twisted the inner workings of your back, I bet your arms would move too.

Wow, turning a BIONICLE's back-gears must be painful.

I expect the gear could be turned by another bonkle, but that the bonkle owning the gear would still have control over their limbs. So it'd be less like Buzz Lightyear's karate chop (where it overrides Buzz's control of his arm) and more like lifting someone's arm up (where their arm could push against yours to stop you lifting it).

I've given this far too much thought.