How email invites work
When you have the sender selected as Participant, then the participant's email client will open up with their recipients BCC'd, and they will see a success message showing that the invite was sent.
If you want to avoid having the participant's email client open up, select the sender as Your Company which means emails will be sent from your company on behalf of your participants.
Note: Many of the actions in the Design section of the Campaign Editor are stubbed, which means you won't be able to perform those actions. For example, you cannot send invites from the Design section.