Often the question you should be asking when you see something like this is not whether the word or phrase in question has ever been used in the way in question by anyone in the past, but whether, in general, English allows words or phrases like the one in question to be used in the way in question.
In this instance, I can see no reason why not.
A vote that takes place after midnight can be an after-midnight vote, or a post-midnight vote; a crowd that frequents an establishment after midnight can be an after-midnight crowd; etc.
If you ask the right kind of question in cases like this, you don't have to know in advance whether a word or phrase is a legitimate instance of a particular species of word or phrase.
There are certainly some nuances and standardized habits of usage that may come into play. A vote that takes place in the morning, for example, would not generally be called an in-the-morning vote, but a morning vote. In the morning-vote example, however, "morning" describes the time sufficiently on its own. In the case of "after-midnight", both words are required to specify the intended meaning.
You can put virtually any word or phrase in front of a noun and turn it into an adjective, particularly if it makes sense as a descriptor and the usage doesn't obscure your intended meaning.
Generally speaking you'll be able to come to the right conclusion with a principled approach, rather than a crystallized-word-function approach.