They were likely dumped overboard so that their manger could be cleared for action. Most ships made a clean sweep of the decks, forward and aft, to remove any unnecessary bulkheads or other construction that could be turned into splinters by enemy shot.

The Shannon was known as a particularly keen gunnery ship, and while they would not toss the livestock overboard in the course of normal sailing/practice, it wouldn't surprise me if they did that before an action. (I haven't read the book, so I can't say for sure where he cites that from.)