If they did, it would be possible to detect the difference with perfect accuracy. Instead, the detectors made by those interested in pushing the concept of "real, natural" diamonds have a false positive rate of 5% looking for the inclusion of things labs could easily add if they cared to
It's much much more complex that a solid sheet of tempered glass, and it catches the light and reflects it in sparkling ways.
Maybe these so called "complex" diamonds create more interesting light interfaces?