The interface shows, in real time, who has received and accepted the invite. However, Hubgets will not send you a notification if your invite email bounces.
When a new contact joins the organization, all the members of the organization receive a notification, while the owner of the organization can see, as all times, the active users, the users who were invited and did not answer the invite and the suspended users.
I have inserted two images below to make these details easy to find.
Hope this helps!