When we talk about the grammar of doubt and uncertainty, we are talking about the use of the so-called
modals, or the auxiliary verbs that indicate conjecture, supposition, or belief rather than established facts or absolute certainty. These auxiliary verbs are, of course, “can,” “could,” “must,” “might,” “may,” “should,” “shall,” “ought to,” “will,” and “would.” When we say “Gina
might dance,” for instance, we are conveying the idea that Gina knows how to dance but we are not sure that she will do so under the circumstance that we have in mind. However, we see no need to state a condition for what she might decide to do.
On the other hand, when we talk about the grammar of conditionality, we are talking about how to convey the idea that a particular action can take place only if a certain condition or set of conditions is fulfilled. For instance, when we say “
If Gina likes the music, she
would likely dance,” we are indicating that it’s likely for Gina to dance if the music suits her fancy. There’s a condition for what she would likely do, unlike in the case of the modal sentence “Gina might dance,” which is simply a supposition or belief.
Based on this distinction between modal statements and conditional statements, we definitely can conclude that modality isn’t the same as conditionality. They are different modes of expression altogether. It would therefore be a stretch if not altogether ill-advised to attempt to make the grammar of modals explain why the conditional sentence below starts with “had” and not with “if” as expected of a conditional sentence:
“
Had Jon joined in an hour after Jess started working, the job
would have been finished in 7 hours.”
The sentence above that you presented is actually just an alternative construction—a more elegant one, I must say—of the so-called
third conditional or no possibility sentence, which denotes a past condition that didn’t happen, thus making it impossible for a wished-for result to have happened. This type of sentence has the following structure: the “if” clause states the impossible past condition using the past perfect tense “had + past participle of the verb,” is followed by a comma, then is followed by the impossible past result in the form “would have + past participle of the verb.”
Thus, the more common construction of the sentence that you presented is as follows:
“
If Jon
had joined in an hour after Jess started working, the job
would have been finished in 7 hours.”*
Note that in third-conditional constructions where “had” introduces the condition, the conditional clause drops the “if” altogether. But whether the condition is introduced by “if” or “had” in a third-conditional sentence, the sense remains the same. In both constructions of the sentence that you presented, in particular, the speaker is talking of an impossible outcome because Jon didn’t join in an hour after Jess started working and the job wasn’t finished in 7 hours.
Such use of “had” instead of “if” for the conditional clause is also an option for the so-called
second conditional or unreal possibility sentence, which denotes a possible but very unlikely result that the stated future condition will be fulfilled; in short, the stated outcome is an unreal possibility. This type of conditional has the following sentence structure: the “if” clause states the future condition in the simple past tense, is followed by a comma, then followed by the future result clause in the form “would + base form of the verb,” as in this example:
“
If I finished my medical studies, I
would be a surgeon now.”
That second conditional sentence will mean exactly the same—and sound more elegant at that—if we use “had” instead of “if” to introduce the condition:
“
Had I finished my medical studies, I
would be a surgeon now.”
RELATED READINGS IN THE FORUM: Modals are not meant for absolute certainties“Should,” “would,” and the other modalsDo better than a calculated guess in handling conditional sentences------------
*Take note that in the result clause “the job would have been finished in 7 hours,” the verb is in the passive voice, so it's in the form “would have + been + past participle of the verb” instead of the active-voice form “would have + past participle of the verb.” 
