Is the phrase "come fast" a grammatically correct imperative? [closed]

It depends on what was intended. To invite people to participate in a religious practice of not eating, “come fast” works but “come quick” doesn’t.

Grammar that doesn’t consider intent is a low bar to cross. If a sentence conveys meaning in some context - any context - it’s grammatical. And some would say that’s already too high a standard for grammaticality.

Let me ease any discomfort you might feel with come fast as an imperative. The source of that discomfort is probably that you think of fast as adjective rather than adverb. It can indeed be an adjective, as applied to a runner, a car, or (in a sexist pejorative sense) a woman. But it can also be an adverb, as in He ran fast.

The horror of using an adjective where an adverb (perhaps one ending in -ly) seems required is often overblown. Before yielding to it, one should remember not only the New Hampshire license-plate motto "Live free or die" but also the opening line of Lamentations in the King James Version: "How doth the city sit solitary, that was full of people!"