Usually, but there are a few exceptions. First, the course must be published for a notification to go out to students when you post an announcement. Second; it's actually a notification about the Announcement and how students receive it depends on their Notification Settings. By default, students get it in their email so in that case the answer to your question is yes. But if they've changed their notification settings they may not receive it by email. Or they might receive it as a push notification on their mobile phone if have the Canvas Student app installed.
Rick
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