I have no formal research on the subject, but, based on my knowledge of plants, I would say that it's possible and depends on the type of inputs. A vast majority of a plant is made of carbon and oxygen, which they get via CO2 from the air. So, if the air is clean, that's a plus. A plant uses nutrients (nitrogen, phosphorus, potassium, etc) to bind itself together. In the natural environment, the nutrients come from the soil (compost, manure, etc) and gets to the plant via water. The soil is just the growing medium so the plant can stand up straight; it's really the water that carries the nutrients. In a non-soil system (hydroponic, aeroponic, aquaponic, etc), as long as the water has nutrients and the air is clean, you have a healthy plant. The light (sun, LED, etc) gives the plant energy to convert the CO2 and nutrients into "food". I don't think it matters to the plant if the light is synthetic or not, just that it has enough energy. LED, of course, is not as good for the environment as natural (and free) sunlight.
My question would be, where do the nutrients come from? If they are using a synthetic fertilizer, then the nutrients are synthetic and most likely not the best for your body. If they are using a natural fertilizer, then I see no health detriment.
My two cents...
- Marie