Meaning and Grammar – Is it All Right to Say ‘All Men Have One Head’?

"Do you think they shouldn't attend that school? What if they would become great musicians?"

This example sounds awkward and mildly ambiguous to me. The ambiguity arises from the fact that would can have the meaning "strongly desire [to]," as in the movie title The Man Who Would Be King. So one reading of the second sentence above is:

What if they strongly desire to become great musicians?

But I suspect that the speaker has a different meaning in mind. Unfortunately that meaning is somewhat obscured by the omission from the second sentence of the intended condition under which "they" would become great musicians in the what-if scenario—namely, that they attend the school. Adding that condition to the second sentence is easy:

What if by doing so they would become great musicians?

or:

What if they would become great musicians as a result [of attending it]?

By introducing the condition into the what-if sentence, we avoid any possibility that readers might read the would in that sentence as meaning "strongly desire [to]." The use of "would become" in place of "became" is somewhat colloquial, but in an informal setting it seems reasonable enough.

"Do you think they shouldn't attend that school? What if they became great musicians?"

Because would has vanished from the scene, the second sentence in this version of the example doesn't have a built-in ambiguity. But the example still works better (I think) if we add the implied condition to it:

What if by doing so they became great musicians?

or:

What if they became great musicians as a result [of attending it]?

Is there any sentence where what if + would is grammatically correct?

It's not hard to imagine snippets of dialogue in which using "what if" + "would" is the most coherent and natural-sounding way to handle a hypothetical scenario. For example:

Person A: I bet you'd eat a whole coconut cream pie right now if you could.

Person B: What if I would?

You have three translations attempting to say the same thing:

1. have drunk freely
2. men have well drunk
3. they might have drunk freely

Your cite gives the verb as μεθυσθῶσιν (related to the Greek word for wine), third person plural, aorist tense, subjunctive mood, passive voice It is difficult to map Greek verb forms directly in English. The aorist was often used for narrative and indirect discourse; the subjunctive indicates possibility; the passive takes the action to the subject. So one literal rendering is "[when] they should [or might] be being intoxicated by wine."

The point of the passage is to examine the hosts behavior when his guests have had enough of his good wine so that alcohol has made them insensible to the quality of further drink.