Not before long he opened the event,two days before the arrival of the mayor.***
How should this sentence be punctuated with the adverbial clause. Perhaps a conjunction or em dash? These types of clauses can't hold together with a comma, right?
Why would you think these types of clauses can't be held together with a comma?
Perhaps you're thinking of a comma splice, which indeed is a grammatical fault. To tell whether or not you're committing a comma splice you check whether the words before and after the comma are both independent clauses (complete sentences with subject and verb). If so then it's a comma splice. Otherwise, it's not. So let's take your sentence as an example:
Not before long he opened the event, two days before the arrival of the mayor.
The first part is "Not before long he opened the event". There is a verb (to open) and there is a subject (he). It's an independent clause. The second part is "two days before the arrival of the mayor". In this case, there is neither subject nor verb. It is not an independent clause and it cannot stand by itself as a complete sentence. Since only the part before the comma is an independent clause you can use a comma correctly: it is not a comma splice.
This is not to say you can't replace the comma with something else (though it is perfectly valid and I would personally keep it). You could, for instance, replace it with the word "just" to emphasize the short time between the event being opened and the mayor arriving. You might even italicize it:
Not before long he opened the event just two days before the arrival of the mayor.
Alternatively you could rephrase the adverbial clause as its own complete sentence:
Not before long he opened the event. Two days later the mayor arrived.
Note that in the latter the second phrase is now an independant clause. There is a verb (to arrive) and a subject (the mayor). It can now stand on its own as a grammatically correct complete sentence.