By tag picture, you mean this?
It would be difficult to have this automatically applied to tag links (or to automatically convert something like [ tag : my-tag-name ] into my-tag-name), because the blog is a fairly standard (as far as I can tell) WordPress installation. (Presumably a WordPress plug-in could be created that provided this functionality).
I don't think it's possible to even add the background image in the HTML view of the WordPress editor (I tried this and it appeared to ignore the inline style).
We could create images ourselves and use those (uploaded images go into a library that's usable for all posts). I'm not sure it's worth the effort, though.