For a fish, the answer as to whether one can eat the fish is based on the simanim (my guess is that they would be unaffected). The same would also hold for mammals. But then there is the issue of whether you a tradition of eating the animal, beyond looking at simanim.
However for both plants and animals, there is the issue of whether one is allowed to breed it yourself, in addition to the question of using it. For example we are prohibited from creating mules but not from owning and using them. If the GMO involves cross breeding different species, then there are some interesting halachic question that will be answered when the practice becomes more common (probably in Eretz Yisrael, since few Jews elsewhere are into farming, and mixing two species is an issue for farmers (American Jews are more into eating kosher animals than raising them).