Yes, it could be an issue. Especially so if your school studies Richard III. Have a chat about it with your teacher. With this major work, in order to succeed, you will need to be prepared to make some sacrifices, as annoying as it can be.
Richard III wasn't the only historical figure that Shakespeare wrote about...have a look through his 'Histories', you should be able to find other historical personalities to focus on, ones that don't overlap with HSC English (Henry VIII for example).
Anyway, good luck!