This is a very good question (and will make for fascinating research) but prior to doing full research, I must say that boxer's have a much better chance of finishing their careers with or later experiencing an onset of pugilistic dementia. Pugilistic dementia occurs in a variety of people whether or not they've actually experienced concussions or are actual athletes.
Pugilistic dementia is not the same as Alzheimer's. Alzheimer's is caused by failures in transporting nutrients to the brain due to tangles in the transport system. Another cause in Alzheimer's is the buildup of plaques that prevents the cells from communicating.
Plaques and tangles are not caused by the blows sustained in MMA and boxing, however it's possible for some boxers to develop pugilistic dementia (aka: punch drunk). It has been noted that there is an enzyme released when one has pugilistic dementia that is also present in forming the plaques for Alzheimer's.
Also, those who have mild cognitive impairment (worse than what's normal for whatever age they are) are at higher risk for Alzheimer's. This being said, I don't believe that it's the sport that would increase the chances of Alzheimers because those who've taken hits in, soccer, football, hockey, even ice skaters who've hit their heads would have Alzheimer's and people who have pugilistic dementia do not all develop Alzheimer's.
One thing going for athletes is the fact that they are athletes. People who are sedentary, are older, smoke cigarettes, etc. are more likely to develop Alzheimer's.