Organic itself no, but when they're organic, they're often also free range, which have more bloodspots.
Organic and free range each independently contribute somewhat to the incidence of blood spots.
Organic hens are often fed varieties of feeds that lead to more blood spots, and free range chickens are exposed to varying temperatures which can also lead to increased blood spots. Scientifically the blood spots we see today, whether on the yolk or the white have nothing to do with fertilized eggs, they are actually simply burst blood vessels in the egg laying process. This is what causes the one or two dots that we see as blood spots.
A fertilized egg has a network of blood vessels running through the yolk. If the embryo dies it can form a kind of ring of blood around the yolk; sometimes the ring can disperse into dots of blood. Those would actually be fertilized egg blood spots. 99% plus of the time today that is not what you are seeing, not even on organic or free range eggs. It’s simply burst blood vessels.
Contrary to popular belief, in just about all egg farming systems, including free-range, cage-free, and organic, male chickens are considered useless. They are all killed at birth, (sometimes by being ground up alive) leaving exclusively female hens on the farm.
Fresher eggs are somewhat more likely to have a blood spot on the yolk; as the egg ages water bleeds into the yolk from the albumen, diluting the blood spot and often diluting small blood spots to the point that they disappear. We all end up eating some blood spots but they aren’t red by that time so aren’t any halachic issue.
By far the greatest determinant of the incidence of blood spots is the fact that all commercially produced eggs are candled. A light shines through the shell exposing any blood spots and those eggs are rejected and never make it to the supermarket. Brown eggs make it harder for the light to make it into the egg, leaving more blood spots that make it through. As many as 5% of brown eggs can contain blood spots. Small organic producers often don’t candle their eggs at all so they will have a high incidence of blood spots that reach the consumer.