Yes, if a kid has a serious illness then teachers are likely to be more understanding. However, if you have the flu, you are almost certainly not going to be able to send an email over the weekend and be back at school on Monday. There are very few serious illnesses that keep you out of school for only one day.
And since this was an oral presentation, I doubt very much that it was a one-day assignment. If I was a teacher, I wouldn’t have much sympathy for you if you had a long-term assignment and didn’t turn it in because you left it until the night before. Plus, the student had the weekend to work on it if needed.