A note from a TEFL teacher. Yes, when "mult" is a determiner, "much" should be accepted, although in affirmative sentences, where "much" is extremely formal, in spoken English "a lot" is far more common. In other words, it is normal standard English. We use "much" more in negative sentences and questions. So I wouldn't necessarily agree that "much" is any more of a standard translation than "a lot".
(See note on Grammar in the second section)
However, here "mult" is an adverb. We use "much" as a stand-alone adverb/pronoun afrer a verb in negative sentences, "He doesn't drink much", but its use alone after a verb in an affirmative sentence would be very rare, and would sound extremely strange to me, a BrE speaker. I don't think many native speakers would say, for example, "He eats much" instead of "He eats a lot". It's the same here, and I don't think "drinking much" would be accepted in any standard EFL exercises/tests.
Note that even here, the few examples of "Drinking much" are mainly false positives, such as "Drinking much more"