The only way that it would effect it is if some of the swelling goes down. It works over several days, so I doubt even a lot of swelling would be down by that time. But even if the swelling has gone down, that wouldn't change anything on the reading.
Here is a web site that discusses the injection of cortisone into a joint in case you are interested in learning a little bit more about that procedure.
If you have any other concern don't hesitate to ask.