How does alcohol affect a person with fatty liver disease? Does it change the metabolic breakdown?

It causes the liver to get fatter.

Alcohol is dealt with mainly in the liver, and it is metabolised and the resulting energy (fat) is stored.

Quick lesson in human energy storage and use. There are two main stores for energy, the live and your jiggly bits (fat). Most tissue can be broken down for energy, but these two are where your main energy stores are. The liver is where you get your first boost of energy, the fat is mobolized and put into the blood stream. Once that is exhausted the body fat/tissue is the next to go.

When you eat it is the liver the is replenished first. Then the body fat stores. Don't think that by just running and running that you will lose weight. That is a completely different topic.

Fatty liver disease is exactly what it sounds like, a rarity in modern medicine. The liver is getting fat deposits. The problem comes when it gets more and more fat deposits. The cells get larger and larger and eventually get damaged. The way the body deals with this damage is by repairing it. So it starts to scar. This is where cirrhosis starts to happen. This is hindering the Liver's ability to work. The main treatment is to, through external means, reduce the amount of fat in the liver.

So in treating fatty liver disease, having a few drinks probably wouldn't be a bad thing, but you're just making your job harder then it needs to be. Imagine a scale. One side is sand, the other is a weight. You need to get into balance. Slowly knocking off the sand until the scale is in balance. You do it day by day. Alcohol adds sand. Making it harder to bring things back into balance.