In Google Apps, when an invitation comes through to a user's email, it adds to the user's default calendar automatically.
Is it possible to have this go to a calendar other than the user's default calendar (a shared calendar)?
No. Shared Google calendars have their own email address. Because the shared Google calendar's email address wasn't invited to the event, it can't 'accept' the invite.
You can manually copy events to secondary calendars by opening the event details, choosing the More Actions drop down, and selecting 'Copy to...'.