Should a comma come before "after"?

The example you have supplied is grammatically correct as you have written it. Your question is somewhat vague because the word after could be used in numerous contexts. The grammatical context is what will determine if a comma is necessary rather than the word itself. The most likely usage of 'after,' in a prepositional phrase, would not require a comma. However, I imagine there are scenarios where a grammatically correct sentence can be constructed with a comma preceding the word.

I finally arrived home, after having driven all day.

A comma before after does seem to put more emphasis on I finally arrived home as the main message of the sentence. Placed after the comma, after having driven all day becomes an aside, a detail to the main emphasis.

I finally arrived home after having driven all day.

Without the comma, after having driven all day is integrated in the main message of the sentence, it has the same importance as I finally arrived home.