Karate itself honestly will not do arthritis any good. But there are other arts that are more suitable for people with arthritis. Tai Chi or any other internal art (Yi Chuan) under a knowledgeable instructor will both provide self defense abilities and aid in healing the arthritis.
I am not aware of anything that can be done to heal arthritis, though I would not discount that certain meditative martial arts like Tai Chi will certainly help with the pain management of the condition so there is probably some merit to what the above poster said. As far as being able to do things, well that is up to the individual sufferer, their pain tolerance level and their willingness to endure. I know that my uncle has arthritis and he can't do much of anything for long, but my grandmother has it much worse and even at 89 gardens and walks and swims and does some aerobics at the YWCA etc. But, and we give my uncle shit for this all the time, she's a tough lady, he's kind of a wimp.
I've been practicing for over 40 years, Shotokan karate, kickboxing, taijiquan and qigong. I have arthritis and pain from a years of abuse. Karate can be practiced but not as explosive as if you were in your youth. The workouts are beneficial as long as you don't go over what your physical condition allows.