I'm not sure either if one precipitates the other, but a number of us on this forum that have or have had cysts also have underactive thyroid .. Connection?
In the future please add additional info to the original post instead of creating a new one. It can get difficult to follow once they get separated.
Many women (myself included) with cysts also have underactive thyroids but we don't know enough to say if one is the fault of the other. I know when I had my cysts that my thyroid levels were all over the place and are now doing much better since surgery.
Do ensure your doctor knows you want to conceive before he operates. I've had the tests on the tubes before due to ectopic pregnancies and it is very easy. It's been about 17 years but I do recall they injected die and could view the tubes on the screen.
Good luck with everying.