I don't know about all disease, but something as fundamental as pH can certainly affect many more diseases than we might guess.
It's not just about pH either. It's about mineralization (leading to alkalinity.) You can get alkaline just by taking lots of sodium bicarbonate, but you won't be properly mineralized, and you probably won't be healthy.
So if you understand the role of minerals in the body you can answer your own question. Can minerals cause healing? Nothing works in a vacuum, but we know vitamins have no role at all if minerals are not present. So what do you think?