Can drinking alcohol while sick cause oral thrush?

Not in particular : There is no scientific causal association between the two that I know of. Are there other infections suggesting a compromised immune system? Is thrush recurring? Are there risk factors for HIV /AIDS infection? A good history and exam is definitely warranted especially if the thrush is recurring.

How sick &with what?: Thrush is not necessarily an std. Thrush develops when the opportunity presents for a compromised immune system. Many patients who use inhalers that contain steroids are at risk, particularly if some of those steroids are deposited in the oral cavity. Patients on broad-spectrum antibiotics, who take steroids for any inflammatory condition, & those fighting a systemic disease (like HIV) get thrush.