I am having the same issue with hostgator as well. I am using this SMTP plugin with several websites and all of them work as supposed to – except one. The settings are correct and the email is sent through the site and host, but not received. I tried this with multiple recipient emails.
However, if I send a test email as plain text, it gets delivered. Looks like a weird issue. I have contacted hostgator and they couldn’t find anything. I hope you can help me with this.