No, these messages do not appear there. Or in any group inbox as far as I can find. Nor in the target user’s inbox. Could there be a site setting that affects this? I looked but couldn’t find one.
There is a private message sent to the user from @system, but it simply states “Your account is temporarily on hold” without any explanation. Its text comes from system_messages.silenced_by_staff.text_body_template, which doesn’t have access to the reason placeholder. The default text is very soft and plain wrong when used as an intentional timeout: “placed on hold as a precautionary measure”
There is a log of the sent email that has the text I’m after, but it doesn’t include the content.
The name of the slug that contains the text I want with the silenced_til and reason interpolation keys is user_notifications.account_silenced.text_body_template — which made me think to look in the user notifications, but it also doesn’t appear there.