Actually this is possible with some undocumented markup for the project description. The markup is a subset of textile (Textile Reference) try this to get an image:
The url can be absolute or relative which means you can use a view as an image (for example !/views/RegionalTest/ProjectThumbnail.png!) . The only challange is getting the correct sizer of image. The markup does not support scaling CSS.
A good idea to be voted up might be to document and extend the markup availoble.
I know I'm a little late in answering this item, but we just got up and running with the Online Tableau product. I was able to take these instructions and create images for each of my project sites without a problem. The key is editing your description for your site and using HTML tags for reference to your logos. The logo must exist somewhere online. In our case, our logos exist within our Feeding America site. So here is one of my descriptions where I have an image for Akron Canto Regional Food Bank. See image below along with text reference.
*Akron-Canton Regional Foodbank in Akron, OH Project Space* <p><img src="https://secure.feedingamerica.org/images_logos/FoodBankLogo_100_275w.jpg" width=75 height=75 alt="Akron-Canton Regional Food Bank logo" /></p>