Alcohol metabolism is not directly related or influenced by the thyroid gland. Alcohol is all metabolized by the liver. However, patients that have a total thyroidectomy can be clinically hypothyroid if they are not given enough oral hormone replacement (with levothyroxine, brand name Synthroid - which is what you are taking), and patient that are hypothyroid can gain significant weight. Patients who gain weight (particularly if gained quickly) can accumulate fat in the liver, which can then lead to inflammation of the liver cells (called steatohepatitis) and ultimately cirrhosis of the liver (this takes years to develop). Patient with steatohepatitis and cirrhosis should not drink alcohol.
Therefore if this is the case, then yes, alcohol metabolism can be indirectly influenced post total thyroidectomy, if after surgery the thyroid levels are not controlled.
On the other hand there are a good number of studies supporting the fact that alcohol consumption decreases the chances of having autoimmune thyroid diseases. Other studies also show that there is a decreased risk of thyroid cancer in patients that drink alcohol (in moderate amounts!).
Hope that answered your question. Let me know if you have other concerns.

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