The campaign will not email anyone on the Do Not Contact (DNC) list, so the contact will not receive any emails from that campaign.
This happens even if the contact is added to the DNC after the campaign launches. A result is that it ensures that if a contact becomes a customer or has some other status change after a campaign starts, but before it concludes, they will not receive emails as soon as they are added to the DNC.
This applies to both contacts (specific email addresses) and domains added to the DNC.
But, the contact will still be on the campaign. This means:
Statistics and performance dashboards will include this contact in the total contacts count
The contact will show as "in an active campaign" on lists of contacts
You cannot delete the contact or merge them (in some circumstances) because they are on an active campaign
To remove such a contact from a campaign:
Pause the campaign
Open the campaign
Navigate to the Contacts step
Find and deselect the contact
Save and resume the campaign