IMO the better way to set up a site before DNS change is to use the “hosts” file method to view the site, rather than the “dreamhosters” method. http://wiki.dreamhost.com/Viewing_site_before_DNS_change
Reason being you avoid the dreamhosters domain for ever getting into your database.
The bad news is yes you will likely need to make database updates to rid yourself of dreamhosters links embedded in your site, the good news is your site will still work while you get that done (provided you don’t delete the dreamhosters mirror too soon).
I actually use a 3rd method that they seem to have dropped from that wiki article. Using dreamhost DNS servers locally. In my case my router handles DNS locally, and I just tell my router to use dreamhosters DNS servers. They likely dropped the method from the article because it can be messy and when changing it on a Windows computer it also means rebooting once when you set it up and once whe your going back to your regular DNS, and if your working on the new site off and on it ends up in a lot of reboots. It only works out for me because my router make its easy and doesn’t require any reboots.
Also just re-read your question: there is a plugin you can use to update the database to get rid of dreamhosters domain name.