If the directory structure of an addon changes can the curse client mess them up when updating?

The simple answer? No, since every time you update an addon with the Client, it deletes the old version than installs the new. But if you are paranoid, then start the Client so it is running with the list of installed addons open. Then browse your hard drive to the addons folder, delete the addon(s) manually, or even better, move them to a new folder. Then click the Reinstall button in the Curse Client and voila~ fresh, new!!

You could even test whether the CC is doing this by looking at the before & after directory structure of an addon using the above method.

Did the old version use to do this too, or is this a new feature in the new version?

I read about problems with the old version not fully deleting the old addons.

@Bidybag, there was a bug during beta where it wouldn't fully delete everything on certain OS's.  That's since been fixed.