I should think not -- at least not in the way you're probably thinking.
The device consists of a wicking layer topped by a light-absorbing layer. This boils water, which produces more or less pure steam. It also leaves the minerals from the water in the wicking layer. If you take distilled water directly away from the device and replace it with fresh seawater, those minerals will build up until the layer is no longer absorbent. On the other hand if all you want is the heat, you run the steam-distilled water through a heat exchanger and return it to the wicking layer, reconstituting the original water.
So it'd probably wouldn't work to use this directly as a steam distiller. However you could use the heat you collect to run a separate steam distiller. That would be very inefficient, but the thing about "renewables" is that conversion efficiency is less important than low installation and operation cost, because you're not paying for your feedstock of energy; any sunshine you don't use would have been wasted anyway. So while it seems physically possible to use this device to power a desalinization plant, whether it makes economic sense depends on whether this is actually the cheapest way to run a plant.