Yes, this is possible- however, please use the following variables for ticket description, last public note, and last private note so that only the text content of the description and notes is sent to Slack; otherwise, the HTML tags will get pushed to slack as well.
- Use {{ticket.description_text}} in place of {{ticket.description}
- Use {{ticket.latest_public_comment_text}} in place of {{ticket.latest_public_comment}}
- Use {{ticket.latest_private_comment_text}} in place of {{ticket.latest_private_comment}}