@ChrisBaldwin ...
Hi there. Maybe??? For the person in question that didn't get the course invitation via e-mail...do you know if that person is able to log on to your school's Canvas environment and see the invitation waiting for him/her on his/her Canvas Dashboard? If so, that person should be able to accept the course invitation there and get into the course.
Another possibility...if you are a Canvas administrator, masquerade [How do I act as another user in an account? - Instructure Community (canvaslms.com)] as the user and then take a look at his/her "Account" >> "Settings" page in Canvas. On the far right-hand side of the screen under "Ways to Contact", there should be at least one e-mail address listed. Does the e-mail address have anything other than the star icon displayed next to it (the star marks it as the "default" e-mail address)? If there is an "!" point icon, this means there might be something wrong with the e-mail address. I believe you can hover over the icon to read a description of the issue.
Lastly, if you are a Canvas administrator, you might be able to use the "Bounced Emails" tool. I'm not 100% sure if this would be helpful or not, but it might be worth trying. How do I view bounced email notifications for user... - Instructure Community (canvaslms.com)
Hopefully one or more of these ideas might help in your attempts to troubleshoot this issue further on your end. Sing out if you have any other questions...good luck!