Can't say I've ever heard of them. I would imagine infertility and ectopic pregnancy would be things that could be affected.
The danger of a cyst in the tube is that it may rupture. At this point you would need emergency surgery and may lose your tube and/or become very ill.
Lat year I had a cyst removed from my tube. Many times when this is done the tube is cut off completely. I had a surgeon that specialized in tubal reversals and tubal surgery to perform my surgery. I went to Louisville Kentucky to have it done. At 43 years old I just had a new baby.
My point is, please educate yourself before you have anything done. There are options out there even though we are not routinely made aware of them.