It only starting showing the text-shaow results when I applied box-shadow to an img. So might be a bug?
It should show, at least, it does in version 13.1 build 6443 (go to Help > About Dreamweaver to check your version).
There may be an error in your code stopping it from displaying in DW. DW is much more strict than standard browsers when it comes to code errors.
Could you post a link to your page?
If not, you could check your css and html against the validators to clear out errors.
EDIT: Just saw your new post, are you talking about box-shadow not showing or text-shadow? Either way, both should show in DWCC. Text-shadow does nothing on images, you need to use box-shadow for that.