A proper answer doesn't seem to have been given in the series (even in the Manga), so the following is speculation based on what we know.
Edolas was the parallel universe where people could not use magic directly, but magic still existed in the form of Lacrimas. While Mystogan reversing the Anima at the end of that arc rendered it completely devoid of magic, it could be that the environment earlier did have enough Ethernano to not trigger the disease.
There are a couple of points in favor of this. First, Exceeds could stay there safely, despite having magic in their bodies. Secondly, the Fairy Tail mages from Earth Land could use their powers on taking the red 'X-Balls' from Mystogan. While we don't know much about them, it's much more likely that the pills allowed them to absorb Ethernano from the Edolas environment, than having enough Ethernano inside them to power all their magic use for the entire arc.
If the description of Face's effects is taken to be accurate, Edolas should currently be inhabitable for mages, much like Fiore would become if they are successfully activated.