Spectators are allowed! If characters arrive too early for their session, for example, they might catch the group that was scheduled ahead of them, or whoever followed after their own. There is a waiting room for characters to hang out in before and after their sessions which includes a view screen of the training facility.

Space isn't infinite, and they wouldn't schedule too many people at the same time so they don't have to wait around, so unless a character is invited to watch by one of the participants, there probably wouldn't be more of a handful of spectators as it would come down to luck of timing.