Yes, you can track the delivery of the emails you sent and also check for email delivery status of those that were sent to you.
You can see the status by opening 'Track Delivery' from cPanel. It's located under 'Emails' section. You can also open that by searching for it in the search option from the top navigation bar.
You can view Success, Failure, Deferred and In-Progress emails from this option. You can filter which you want to view and which you don't. You can see in detail why the mail wasn't sent in 'Results' option. You can see further details under 'Actions' column. Simply press on info icon for whichever email details you want to view.