This scenario is supported since
4.1 release. See the release notes (follow that link) for a short explanation and an example (see
(F) Sending custom data back to the client after a CallBack (DayPilotCalendar & DayPilotScheduler)). A working example can be found in Demo/Calendar/Default.aspx/.cs.
Basically, you call DayPilotCalendar1.Update("Your data") and load that string in AfterRenderJavaScript on the client side.