No, it is not common for a dog to have high liver enzymes with addison. This may be a symptom that the dog eats half cooked or uncooked food with high amount of salt content.
It is common that dogs with addison's have their kidney values and liver enzymes raised up. It is better to check the biochemistry levels of the canine's blood. Treatment for addison's can be continued along with the treatment for liver disease.
It does not appear to be common. However it more common to have problem with the adrenal glands and electrolyte imbalances. It's more of a thyroid problem.
