After dicking around with the API for a while I found that that you can highlight/dim tabs using chrome.tabs.highlight running in a background script of an extension. Maybe I'll spend a little while tomorrow making a more complete version.

The Great Suspender, which actually suspends the processes of these tabs, very useful if you have lots of tabs

https://chrome.google.com/webstore/detail/the-great-suspende...

Yes it suspends the process, but doesn't visually indicate this by fading/sorting the tabs for you. At least, not the version I used a year ago. (edit: it does now!)

For me it fades the favicon slightly

http://i.imgur.com/y1xSEtF.png

To be fair the suspend feature is the killer here

It visually indicates it by replacing the site's favicon with the app's icon. If you see blocky face, your tab has been suspended.