Can I silence alarms from shared calendar (on a calendar-by-calendar basis)?
This answer's for iCal, since I don't have BusyCal, but I would assume that it has similar functionality.  Hopefully, it can help you to find the right control, even if it's not exactly right.

In iCal, you can right-click on a shared calendar in the calendar list and Get Info on it.  In the dialog that pops up (see picture), there's a checkbox to ignore alarms.



I can only assume there's something similar for BusyCal.