This question has not been answered specifically, but we have somewhat addressed it at a higher level. In the CAP project mission statement, we have language that mentions that we will not change the existing game and mechanics of Pokemon, we will only add to it. If egg moves were passed, that effectively changes existing pokemon movepools.Did we come to a conclusion on the "adding new pokemon unlocks new egg move chains" problem? I seem to remember one of the members recommending that egg moves only being passed to the pokemon, not from, but I haven't seen any official rulings on it.
Therefore, CAP pokemon cannot pass any egg moves.
However, this question has made me consider altering a few phrases of the mission statement to make this general concept a little clearer. Right now, it refers mostly to mechanics, and not the pokemon themselves. I'll probably propose some wording changes in the mission statement workshop thread. If you wish to comment further on this issue, do so in that thread.