Should an elderly person with peripheral neuropathy occasionally go barefoot to improve balance or sensation?

Not sure will help. Going barefoot in and of itself will not correct for the neuropathy. If you have diminished sensation in your foot it will open the possibility of stepping on something sharp and injuring yourself and not knowing it.
Balance. Since peripheral neuropathy reduces position and pain sensation it is important that the surface that you walk on, be free of impediments so as to prevent inadvertent injury. Balance involves signals from the brain, the inner ear, the perpheral nerves , and even our vision. It may be helpful to retrain our brain and the balance mechanism in our inner ear with tai chi, and standing on one leg, .
I think. Improving balance at an established balance center (physicall therapist) is a wiser idea.