Is it appropriate for me to ask the leader for leave like this? Would it be rude?

Generally speaking, it is enough to ask for leave and explain the reasons. However, it should not be a day or two for you to ask for leave in this situation. I think it is necessary to tell the leader in person during such a long holiday, so that the leader has time to accept and consider who will take over the work during your absence. It's a bit impolite to simply send a message asking for leave. I hope it helps you!