I know of no targeted research that addresses this question. Here at Tufts University - where many of our exercise studies recruit elderly volunteers - over the years we've had a number of participants who suffer from Parkinson's. We find they do very well working with an experienced trainer. They become stronger; their balance (which is impaired by the disease) improves; they experience a generally improved sense of wellbeing. Unfortunately, we don't know how long these benefits last, or if they could actually reverse the effects of the disease over time.
When someone with Parkinson's disease asks me about strength training, I tell him or her to discuss the possibility with their doctor. I also urge them to work with an exercise physiologist, physical therapist or personal trainer, so they can select appropriate exercises and make sure their form is correct. And I remind them to pay attention to their body - feeling good is the best indication that exercise is beneficial.