With great appreciation and permission of Mike Bombich, the guru behind the awesome CCC software, here is the (complicated!) answer. Hope this helps others who were wondering about this.
"Good question! It's a bit tricky to answer, it depends a little bit on the format of the disk image (dmg vs. sparesimage vs. sparsebundle), what kind of changes occur while the task is running, and whether the diskimages-helper service has any exclusive locks on the disk image file or its components. Whenever you make a change to a mounted disk image, though, those changes are nearly immediately applied to the underlying storage. The changes are buffered a bit in memory, but generally you can expect them to be applied to the disk image file. If you make those changes while a task is running, though, then just keep in mind that CCC creates a snapshot of the source at the beginning of the task and uses that read-only snapshot as the source for the duration of the task. Changes made to the source while the task is running are not reflected in the backup.
The main sticking point with mounted disk images, though, is that the diskimages-helper service will apply exclusive locks to the dmg or sparseimage file, or to band files within a sparsebundle disk image. Those locks will prevent CCC from opening the file or its components (and naturally CCC will present an error in those cases)."
(PS I wanted to mark this as the answer, but for some reason, it's not letting me.)
