Can it breathe?

Yes.

Turtle Coat Architectural Coatings are tested extensively by labs like BASF for “Vapor Permeability”. Vapor Permeability is a ¬†measurement of the amount of moisture that is allowed to pass through the Coating. Turtle Coat exceeds the amount of permeability of most any other coating. The result is that the surfaces are allowed to dry out and does not trap moisture behind the Coating.

The Testing Results are listed on this website.