No.
If you test the genetics of a population they will fall into clusters of similarity. These clusters are what we call families. They are real and based on an outside thing. Nations only exist so long as we mostly agree they do.
That is not to say there are not aspects of family that are social constructs (e.g. adoption) but rather that as a category they exist independently of their social existence.
So nations are not made up of these families? But what is a nation made of?
How exactly do you define a social construct?