Is there a way to automatically convert the relative urls to absolute? For example, when uploading an image it is automaticlaly included as a relative url, so it doesn't appear in the html email when received. Is there an automated way to change this or does one need to go in the source of the newsletter and change the url for all image/link instances?
Pathologic input filter will do that for you.
Pathologic is an input filter which can correct paths in links and images in your Drupal content in situations which would otherwise cause them to “break;” for example, if the URL of the site changes, or the content was moved to a different server. Pathologic can also solve the problem of missing images and broken links in your site’s RSS feeds.
Download and install the module, and then enable it for the text format you're using. It also supports the feature to bulk update your existing paths.