If a person with bad vision uses manual focus on a camera, can the focus be adjusted to their own prescription?

Disclaimer: I'm not an optician. I do, however, work in advertising and happen to have a number of clients in the lens manufacturing industry. Take what I'm about to say with a grain of salt.

Short answer is, not really.

Diagnosing vision issues is much more complicated than simply "is it in focus". The shape of the cornea, how your eye physically reacts to light, distance from an object, and disease all have an impact on how you perceive the world around you. That's why you have things like aberrations, glares, near sightedness, far sightedness, and a plurality of other vision problems. When someone is fitted for glasses or contact lenses, a number of parameters (read, dozens) are required get what is considered a proper "fit".

There are some similarities between how a camera lens works and our eyes, but you also have to consider that you're not just looking through the lens itself, you're focusing on a screen that's attached to the lens. So, if you can't focus your eye sight at the distance the screen is at, it doesn't matter what the camera is seeing, because it'll look like garbage to you either way.