It's definitely possible, but how easy it would be might depend on several factors.
Firstly, are you trying to do this without modifying or adding any code to the theme or plugins? ie. Are you purely a "user" or are you capable of doing some coding yourself? If you can't find a plugin or theme that does what you want, then you're gonna have to write some code or get somebody to do it for you.
If you want a starting point, I'd say that what you want is probably some CSS to add the icons to the tabs. This is assuming that you've at least successfully got the tabs to work. Adding icons to tabs would be very easy for most web developers (Hint: CSS background property). But then there's the added complexity of how to choose which icons go onto which tab. Are these icons going to be pretty much fixed, or do you want the icons to be selected by the user when editing the content?
There are a lot more questions I could ask, but really what I'm saying is that in order to give you a better answer, I'd need to know a lot more detail about what exactly you want to accomplish, and what your skill level is.
Hope this helps a little.