Saving the state is difficult because the group doesn't have any id, it's an ad-hoc client-side group. Moreover, it's not guaranteed that the group will have the same members after .update() as the events are reloaded.
There is also a somewhat similar concept called "joint events" which lets you group events using an id and move them together:
http://java.daypilot.org/sandbox/Scheduler/EventsJoint.jsp
Theoretically, such a group could be collapsed but I'm afraid it's not exactly what you are looking for.