Yes, Quick Fields can definitely handle this.

We simply need to take a sample email and find the location of the subject on that email. Then set up some other criteria to have the beginning of each email be identified as a new version of that document class and then in the page processing set the contents of that location of the subject line to be a token and use that token in the document class definition's default template/fields. 

In this instance I will assume you want to take all emails from the repository, so you will need to use the Laserfiche Capture Engine to grab from inside the repository. If you have an email template that you set all emails to, then you can have Quick Fields perform a search for those emails without certain fields filled in and have it act upon those. Just set it to store to it's original path and retain the original name and you should just be adding content to these files and not moving them around from where they need to be or overwriting anything you shouldn't.

EDIT: Please note, the best way to make use of this type of session is in the Quick Fields Agent way as you can automate this process to run at the best time of day or throughout the day and make instant use of the emails saved to the repository.