Can I use my account and my site even though my domain name hasn't propagated yet?

Yes, you can use your website without a domain name (requires hosting).

We provide you a temporary URL in your welcome email, which can be used to view your site when your domain name is not working.

cPanel (Linux) example: http://ipaddress/~cpanelusername/

Plesk (Windows) example: http://ipaddress/$sitepreview/domain.com/

Of course, this is only an example. You must replace ipaddress with your server's IP, replace cpanelusername with your actual cPanel username, and replace domain.com with your actual domain name.

Note: If you forget the trailing forward slash (at the end) the you could be redirected to a different URL.

Yes, you can use your hosting account without a domain name.

We provide you a temporary URL in your welcome email, which can be used to manage your hosting when your domain name is not working.

Shared Web Hosting: http://ipaddress/cpanel
Reseller and Linux Dedicated Hosting: http://ipaddress/whm
VPS Hosting: https://ipaddress:4643
Windows Dedicated Hosting: https://ipaddress:8443

Of course, these are only examples. You must replace ipaddress with your server's IP.