Hi,
Go in the menu Customers>Emails history and you'll see a list of all the emails sent by HikaShop.
If you see the email there, then HikaShop sent it.
So all that's left is either your sending email server not sending it (because of encoding, format, embedded data limits, etc) and in that case you have to check the log of the email server for the error which will explain why the email couldn't be sent; or the email was rejected by the receiving server, most likely for spam reasons (and you can use the
www.mail-tester.com/
website to check on that).
So the blacklisting could be the reason, but it might be something else. It could even be several different things.