I just tested this on the demo and no, the option "Remove accents from question URLs" doesn't remove accents. I don't think this will be possible because the username is the "key" to the page - i.e. the string "küçük" is looked up in the database, not a user ID. You'd need major changes in the code behind to do this.
Although it does look fine in Google Chrome, the URL shows as /user/küçük