A cyst cant prevent pregnancy, as you can still ovulate from the other side. A cyst is caused when the egg prepares to be released, but doesn't pop off as it should and instead it fills with fluid or blood. When I had cysts it prevented my period from coming, though. Most of them resolve themselves, only when it's larger do they worry about things like the twisting of the fallopian tubes.
I was told by my doc that cysts during pregnancy typically resolve themselves after 12 weeks, and are pretty common. Especially if it's the corpus luteum cyst--everyone gets that. Before the placenta takes over its a main source of progesterone.