Mark Thoma quotes George Evans,

First, because it is a carefully developed, micro-founded model incorporating price frictions, the NK model makes it possible to incorporate in a disciplined way the various additional sectors, distortions, adjustment costs, and parametric detail found in many NK/DSGE models.

No! There is no specialization and trade in these models. You can call such a model “micro-founded” all you want. It isn’t. These empty modeling exercises do not deserve to be called micro-founded. They do not even deserve to be called economics.