Hello! Yes, I think this is a common use-case for Connect users.
Have you seen the Connect admin guide? There is a ton of useful information there to help you get started.
In particular, I think this section will be profitable for you:
The Server.Address property is the public URL used to access the server. When accessible over a non-standard port, this URL must specify both hostname and port. This setting enables Connect to include links in emails that send users to the appropriate location on the server.
...
Here is a sample configuration specifying both SenderEmail and Address.
[Server]
SenderEmail = rstudio-connect@company.com
Address = https://rstudio-connect.company.com/
You might want to be aware that if you do not set up an Elastic IP or a Route 53 URL or some other way of routing traffic to a consistent location that you might have to change this configuration when the box is reset (and the AWS URL ec2-... changes).