Turkish coffee is mostly served without added milk as that's how most people like their Turkish Coffee to be served or drank.
But if you want to add milk to your Turkish Coffee you can do so and it will add some better taste to the Turkish coffee.
There's no rule that says you can't or can add milk, creamer etc to your Turkish Coffee so if you want milk or creamer in your Turkish coffee for flavor you can do so if you want too.
I drink Turkish coffee once in awhile and when I do have Turkish Coffee I do like adding some milk to it or some creamer.
I find the Turkish Coffee is more enjoyable and tastier than drinking the Turkish Coffee without it.