So, my etiquette question involves tickets. If Emma ends up joining us, do I need to offer to pay her ticket?
No, you do not have to buy Emma's ticket.
This sort of situation is similar to my workplace, which often offers discounted baseball tickets to all employees. Co-workers then go around and ask, "are you going? Can I sit next to you?" Other times co-workers even say to others, "Susie and I are going. Do you want to join us?" It's just a fun, informal event that we're all invited to.
Emma most likely has no idea you are buying Jan's ticket.