In the Core Data lecture from Stanford 193P iPhone course on iTunes, the instructor coded up a sample project with Core Data without using NSPersistentStoreCoordinator
Without a persistent store coordinator you will be unable to save your results to a persistent area (database, file, etc)...so if you want a persistent data manager that is utterly useless, then omit NSPersistentStoreCoordinator. Are you sure the project wasn't using it? How was the professor saving the data? When you create a new Core Data project, this logic is autogenerated for you.
EDIT: I got it now, the professor is using UIManagedDocument, which uses its own persistent store coordinator internally (based on the file type) so there is no need to create an explicit one (unless you are not satisfied with the default). So, in the end, its not about whether or not to use a coordinator, it is whether or not you explicitly create it.