Yes, you could certainly do it that way. That's basically the purpose of a "robin" so everyone helps everyone out. It's somewhat of a take on a mystery quilt, you don't know until it's all put together what it looks like, beyond the basic instructions, so if you're really flexible this is a great way to get a wonderful project made with many hands.
There are varying ways of organizing it. I just googled and read different ways it can be done.