Yes, all reports enforce global exclusions if they are turned on in the report criteria.
While you are able to toggle the enforcement of your custom exclusions (found under the Report & Communications Exclusions area), our reports do not allow you to toggle the enforcement of core-mapped exclusions. If you need this message to go out to those that have a core-mapped exclusion (such as DoNotMail), then you will need to use the 'Mandatory Message' category for your template's Communications Category. This will tell Core iQ to ignore all exclusions and send the message to those individuals regardless of opt-outs or other preferences.