It will most likely still work, but there's also a chance that it won't. No one can say until someone has tried it and even if you find someone who can confirm that it works for them, you should still be cautious as there is no guarantee that it will work for you.
CourseNotes looks to have been abandoned by the developers. There have been no further updates on the app's site or the developer's twitter or facebook accounts since 2014.
This means that you should really think about how important the content that you have input into the app is to you and for how long you will want to continue to access it. If you have invested a lot into it and you want to continue to access the information long term, you need to look at how to migrate your data out of it and into something else.
If you still want to upgrade your OS, you need to ensure that you have a backup that you can revert to if you find that after you update CourseNotes doesn't work.
The simplest thing to do is to create a bootable image of your computer's hard drive onto an external hard drive. You will need an external hard drive that is at least as big as the space taken on your internal hard drive. You can create the image by using an app like SuperDuper or Carbon Copy Cloner. Once the image backup is done, test it to make sure that you can boot your computer from it.
Once this is done, you can complete the OS update and confirm if the app still works. If it doesn't, boot from the external image drive and clone it back onto your internal drive.