Can I prevent a user from receiving any messages from the helpdesk?

The help desk sends out automated notifications to agents and users.

You can find a list of the different types of messages sent by the helpdesk plus how you can turn them off in this KB article.

There are some messages though, that cannot be turned off. In order to prevent a user from receiving any messages from the helpdesk, go to Admin Settings > Users. Search for the user. Click on their profile, then on the pencil icon on the upper right to edit. Click on "More information". Here you'll see a check box that reads "Do not send emails to this user. Ever." Once checked and save, no messages will be sent to the user.