No. That's the point. Only the parent theme is updated, so your child theme is not overwritten. However, any changes in your parent theme that have not been overwritten in the child, will become effective.
So, say for example that an update makes a change to a template file that you have not altered (by creating a child theme version located in your child theme's directory). Those changes are automatically implemented, because WP uses the parent theme's template files when the child does not provide an overwritten version.
Similarly, all changes to functions in functions.php will be implemented for all functions not overridden in your child's functions.php file (if it has one).
So you get the best of both worlds.