>As you correctly indicated, I am getting "::1" for IP when running on my local Web Site. Do I understand that when I deploy the app to the customer web site (and they will hit it not from local web site), I will see valid IPs?

You will see a valid IP if your site responds to the Internet.

Note that you might get multiple occurences of the same IP for various users, assuming those users are from the same company going out through the same proxy.