I'm certainly living proof.

It's pretty obvious that if one has neuropathy affecting one's motor nerves one will lose strength and function and this will have all sorts of effects. But even if one's condition is entirely sensory, one can still have them. The disruption in proper sensory feedback, both fine and gross, can cause you to have the dropsies, the tripsies, the bangintothingsies . . .

The degrees of this vary person to person and day to day, but I've had plenty of days when things are just jumping out of my hands, and when stationary objects are mysteriously moving into my path.