That's what common decency would suggest, yes. There's ways to do it of course, and one should confer with wiser people around them on how to do it. If there is a hospital full of 100 dying patients, and I offer one of them the chance to go viral (maybe they just have some viral quality that others don't), I would hope that one person doesn't take it. The whole thing is very somber and needs to be handled in that way. Nothing about this is easy, and I am suggesting modesty in the face of suffering.
Comedy might be the best analogy. There are ways to do it around sensitive topics. The go-ahead to do something is not as simple as "well I think it's funny", or in this case "well I'm the one that's dying".