What happens then?
Do-support is a syntactic rule. As such, it has conditions and constraints for its application. Do-support is required only where another rule (like subject-auxiliary inversion, or negative adverb) requires an auxiliary verb, but there is no auxiliary verb to hand.
In that case, English produces a meaningless do that behaves like an auxiliary verb (in fact, it behaves like a modal, since it has to be followed by an infinitive verb form, and it has to be the first auxiliary, (because there weren't any other auxiliaries, duh), like modals do. But unlike modals, it has no meaning at all and merely facilitates the inversion or contraction or whatever.
- Bill eats asparagus ~ Bill doesn't eat asparagus. ~ Does Bill eat asparagus?
But these are not imperative constructions. There is no requirement for an auxiliary verb in an imperative sentence. Consequently there is no requirement for Do-Support to apply, and no evidence of its having applied. Granted, do can occur in some varieties of imperatives. But that's not Do-Support. There are other varieties ('readings' or if you prefer, 'flavors') of do, rather like deontic and epistemic readings of modals, beside Do-Support do, which the simple verb has mutated into.
One of them is the so-called "emphatic do", as in DO be quiet now!, or Do have a little talk with him, won't you?. Another is the pro-verb do, which can stand for just about any verb (but not many predicate adjectives or nouns)
- What he said to do was to stand there/sing the blues/be back in 1 hour/*be tired
Then there's Ross's
ACT do, which is restricted to syntactically active verbs and often takes noun phrase objects describing the activity
- I don't know how he finds the time to do it/do carpentry/do the work.
Do, like let, and sense verbs, and aspectual verbs like try and manage, are "small verbs" that don't follow the rules for big verbs with meanings; these guys sneak down the aisles and get into all kinds of trouble. Like kids