I think it has some influence. Yes he has severe parkinsons but the constant barrage from headshots had to have played a roll in his condition. As far as it causing parkinsons, no, but does it have something to do with his mental state and motorskills yes.
His motor skills are because of the illness. His slurred speach also has something to do with it. At the Hall of Fame dinner in LA when I was with him he was slow in moving. In fact I cut his steak for him. When he went up on stage he needed some help. He started his speech off slow but about a minute or so into it, if you closed your eyes you would have thought you were at an Ali press conference in the 60's or 70's. He went off with the mike. He was awesome. It gave everyone goose bumps and several people were crying. It was just unbelievable when he spoke and how he spoke. The place went crazy after that.
I remember walking with Jake Lamotta and saying to him if he felt sorry for Ali. He told me that "don't feel sorry for him, he has led a life that no one else can ever dream of. He is the champ and always will be".
I do think the punches did do a little to his speech. But nothing to his mental state. He is still quick thinking just his body can't keep up. His wife told me 3 months after this pic in Miami that Ali had more funwith me than she had seen him have in years. He tackled me and we went rolling on the ground. He is very solid. He was weighing about 235 he told me.