Yes, frankly, it will. It will make them possible.
As it turns out, the AMA hasn't suppressed any cures of anything--read that, cures that really do work. What it suppresses are quack cures, causing the quacks to augment their income and their visibility by making unsubstantiated claims that their "cure" is being suppressed by the AMA to bolster the riches of the medical industry.
Capitalism not only provides the funding for developing the tools to cure diseases, it motivates it. Let us not kid ourselves, here: if you've got the cure for something, you're going to make a bundle off it, using the legitimate structure of the current medical system.
What, you say, of the cures found outside the system?
Chuckle--I rememeber a lot of 'em. They all got ditched when someone (inside the system) found something that really worked for the disease process, or when grieving families realized that the cure wasn't working and publicized the fakery widely enough.
So, yes, Capitalism will affect the curing of all sorts of diseases--it will continue to drive the search for the cures, and will continue to find the cures.