In the accepted answer to the question that I asked, Would Voldemort have been recognisable to the average wizard? It is agreed that most wizards knew what Voldemort looked like. They may not have seen a perfect image of him, but it has been agreed that Order members and Ministry people not trying to hide his reappearance would surely circulate his most defining features. The strange snakelike elements of his appearance would surely be the first thing to make others aware of.
This being the case, I am sure that many would make comments about his lack of nose. Add in the fact that many people (especially in Great Britain!) use humour to hide pain, tension and anxiety, I'd be willing to bet that at least some wizards would joke about Voldemort's appearance.
On a side note, I think the comment is primarily aimed at the audience of the show. The Internet is full to bursting with memes on Voldemort's nose, we like to see images of Ralph Fiennes in full makeup but with his nose still attached - I'm sure it's mostly aimed at that. Not the greatest thing to include in your special theatre show, but a little nod that I'm sure some people think is the height of great writing.