It is possible to change the behavior of an engagement based on the status of your agents.
If all your agents are at capacity or offline, the engagement can be configured to behave differently by enabling an offline survey. In the Engagement Portal, go to the Campaign Builder, edit an Engagement and advance to the Engagement studio. Select the dropdown to configure the Offline settings:
Now, when no agents are available, the engagement will present your visitors with a web form, instructing them to "Leave a Message".