Is it possible to turn off the iPhone Calendar invitations badge/list?
Actually, this functionality has been moved into the Notification settings for Calendar items (Settings > Notifications > Calendar). 

In that view you'll have the option to change notifications for: Upcoming Events; Invitations; Invitee Responses; and Shared Calendar Changes. Each one give the ability to select: whether its shown in notification center; notification sound; badge app icon; show on lock screen; and the alert style!