What are effects of alcohol on a previously damaged liver?

Probably harmful. Alcohol is toxic to the liver. Depending on the extent of previous damage, the reason for the damage, and whether or not the liver was able to recover fully, alcohol could do real harm.
More damage. The already damaged liver is far more sensitive to the toxic effects of alcohol. The combination of hepatitis c and drinking alcohol is particularly nasty - the death rate for people who have both conditions is much higher than would be expected. In addition, inability to stop alcohol when you know it can hurt you is a sign of alcohol dependency. Get help to stop. Liver failure is awful - don't!