No, adding the domain as 'fully hosted' will not request a domain registration transfer, it will simply create a web-directory inside your users home-directory for the domain and configure Apache to handle requests for the domain.
Firstly, configure the name servers for your domain at your registrar (GoDaddy) to point to the DreamHost name servers...
If your registrar only allows you to enter two name servers, simply use the first two.
Once this has been done, you need to add the domain to the DreamHost hosting system as 'Fully Hosted', I think you already know where to find this in the panel. This will create a web-directory for the domain in your home-directory. It is this web-directory that you need to upload your site files to.
It can take up to 72 hours for the new DNS information to propagate across the Internet, but once this propagation has completed you should be able to access your domain via a browser.
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