"Do you drink any tea ?" should be more or less correct
More or less, yeah, but technically the word "any" wasn't in there, even if your translation of the sentence had a similar meaning.
Why can't it be Boisez-vous du thé?
Correct me if I am wrong but "boisez" is not a conjugation of "boire" in the imperfect tense
Does this also mean "Do you drink tea?"?
why not : would you like to drink tea?