Is someone who is @mentioned in a direct message conversation they are not in still notified?

My Slack application (version 3.2.0 from the App Store) is running on my MacBook (running High Sierra 10.13.5).

I send direct messages to Persons A and B (I have invited both of them to the same direct message thread). In the message thread, I mention Person C by using @person_C. Is person C notified by the mention and will the message thread then be visible to person C?

I've just tested this. Private messages are only visible to the people in the private conversation - if someone is @mentioned and they are not in the conversation, they will not see the message and will not be able to view other messages in the conversation.

That direct messages using @mention do not send notifications is also stated at the bottom of Slack's "Mention a member" documentation:

Tip: Using an @mention in a direct message with any member will not trigger a notification.

Additionally, since you cannot share messages from private conversations, the only way to share a message with someone outside of the conversation is to copy-paste it into a separate message to them.

So no, person C would not see the chat message with the @mention or any of the other messages in the conversation.