Hi,
Yeah it is by design. A stagger method in a timeline returns a TimelineLite instance with a TweenLite instance for each element in the array passed to it, and since getLabelsArray is a method of the TimelineMax constructor you're getting undefined.
Also keep in mind that, besides the parameters of each stagger tween passed in the stagger method, you have no further control over those instances created by these methods. If you want to place a label where each stagger animation starts, you might want to take a longer road and use a loop in order to create each individual tween and place the desired label inside a TimelineMax instance.
The current code you posted, only gives you the possibility to add a label when the first stagger tween created by each stagger method starts.
Beyond the fact that:
console.log( children[i].getLabelsArray ); // -> undefined
There is not much I can infer from that code. Perhaps you can provide a few more details in order to get a better grasp of the roadblock you stumbled in your code.
Happy Tweening!!