Answer:
Thrush is a yeast infection that can occur in the mouth, throat and vagina. Drinking alone does not cause it, but the nutritional deficiencies* that go along with alcohol abuse and alcoholism could certainly contribute to immune deficiency that could allow thrush to develop. Frankly, if you have thrush it would be a good idea to see a doctor about some follow-up tests.
*Alcohol prevents nutrients from being absorbed and utilized properly. All alcoholics suffer from vitamin and other deficiencies.