In general I would not recommend overwriting the contruct on any object in Yii.
I know its a bit counter intuitive, but Yii works around conventions, and a convention here is to just put you initialization code in the init() method.
If you want to take a look at the Controller's source code you'll see that I does a lot under the hood, it needs to check for themes and controllers folders to resolve the view's path.
This mostly happens in the render method. but as rule of thumb, stick to the init() method.
Just stick to the convention and you will be fine, I can't think of a case that wouldn't fit well to just put aditional logic in the init method. its not like you are passing paramenters to the contructor, is it?