If I enable Automatically close unresponsive conversations using rules, will it trigger a survey?

Hello @user619​ 👋, Welcome to Interconnect ✨

As far as I know, once the conversation gets closed Intercom should send a conversation rating request.

Keep in mind that their several criteria during conversation rating sending:

Operator only sends conversation ratings at the right time. A rating appears when a conversation matches the following criteria:

• The conversation was replied to by a teammate.
• The conversation is over 250 characters (including spaces, and replies from your teammate and customer). This helps ensure ratings don’t send for short conversations.
• The conversation is closed within a week of the last reply. If you or the customer hasn’t replied to the conversation in seven days, we won’t send a conversation rating, to prevent them from appearing on old conversations.
• It's not a group conversation. Operator will not send a rating request when more than one user/lead are included in the conversation.
• A rating request hasn't been already sent in the conversation. Operator will only send a rating request once per conversation.
• A user/lead started the conversation or replied to an ongoing message to visitors. Operator won’t send a rating request on conversations started from messages sent to Users or Leads, or Custom Bots.

More information about this topic can be found here.