R' Yosef Berger told me not to learn the latter half of Mo'ed Katan while both parents are living. This was to learn through the sugyas of the gemaras, not just to learn the laws of aveilus, and he said not to. The question I asked him was about if the group I was learning with should begin this topic. He said that it should be done in private. He seems to have held of the Knesses HaGedolah in Yishai's answerYishai's answer.
R' Moshe Heinemann also advises people not to. There is an old "legend" told in Ner Israel, which I never confirmed, that R' Heinemann had a small chabura of 5 guys who wanted to learn hilchos aveilus with whom he began studying. Over the course of a year, 2 or 3 of them had a parent pass away. R' Heinemann cancelled the chabura.