Absolutely! In fact, we recommend not allowing local changes in most use-cases. This helps with streamlining your editor’s processes; the more sites your editors have to visit, log in to and manage, the more complicated their work becomes. By reducing the number of sites your editors use for content entry, their work becomes significantly easier and more efficient.
But if you only have a handful of sites or they don’t share the same content this may not apply to you and you’re better off allowing local changes.