What HawkOpen does: every email it sends or prepares ends with a “Do not send me messages” link in the language of the email, and emails sent from your connected mailbox carry List-Unsubscribe headers. The link does what it says: the address gets no further email from anyone in your company through HawkOpen, marketing or not; campaigns skip it and single messages to it are refused. Emails you send outside HawkOpen are not affected.
Because the link also stops service messages sent through HawkOpen, plan another channel for messages you must still deliver, such as invoices or contract notices. The link and headers alone do not show that an email meets the rules.
Withdrawing consent to tracking is a separate step: the link in the tracking notice turns tracking off without unsubscribing. Where rules that require consent apply, tracking may start only after that consent has been obtained. The link in the message lets the recipient withdraw consent later.