If I delete an appointment type, will this delete the existing appointments of that type scheduled in the calendar?

No. The system will remind you in a pop-up window that there are appointments linked to that type and will ask you to confirm the deletion. If you say "yes", the scheduled appointments of that (deleted) type will remain in your system, but they will be re-linked to your default appointment type.

If you are not sure what your default appointment type is (because you might have edited it in the meantime), you can run a test (by creating a fictive appointment type, scheduling an appointment of that type with a test client, deleting the appointment type, then going back to the test appointment in edit mode and observing the type it was re-linked to).