I think that would be a great idea. It would have to sort of be like the stock market thing, though, because we would have to have a scheduled time to do it. I think it would be a cool idea to combine the relay race with the Arcade challenge that was briefly mentioned in the CI&D. Here's my idea.
Everyone interested gets into teams of like ~3. Then, a game is randomly selected from: RBY, GSC, RSE, or FRLG. That will be the one that we all play. So, a team member will be selected by the two of us from each team. That person will play through the first gym. Player two will be selected by us. We will give like a week for player one to transfer to player two, and for him to do through gym two. So on and so forth.
Now the arcade part of it. Starting with the second person, and continuing until the game is completed, I will have a random series of events that can happen. They can range from: No items this time!, a friend wants you to help train his Flaafy. Flaafy must be at least level 25 before your section is completed. Here's the code to get a Flaafy., Oh no! Your first Pokemon is sick this round. You can't use the first Pokemon in your party this time.
Stuff like that. I will randomly select one. What do you think?