Is it actually possible to send a message if the account is offline? Here's a section of an article https://support.zendesk.com/hc/en-us/articles/4408842880282#topic_d3p_q5f_rhb that clearly says it won't work if the account is offline...

Trigger actions

Action statements define what occurs if all the condition statements are true and the trigger fires. You can think of action statements as ‘then’ statements: if all of your conditions are true, then perform these actions to update the user and optionally send notifications.

Table 3. Trigger actions
Action	Description
Send Message to visitor	Sends the given message to the visitor Note: If the account is offline, this action will not work.