Hanzou
Grandmaster
Karate's Grappling Methods: Amazon.co.uk: Iain Stuart Abernethy, Peter Skillen: 9780953893201: Books
However broad or narrow your interpretation of "grappling" is I think you would be hard pushed to argue that not one single chapter of this book covers something which falls within your interpretation of grappling. The conclusion therefore is that karate does include grappling.
How much of it you consider "grappling" and how much you do not, is purely a personal choice based on your interpretation of course.
Yeah I quoted the author earlier. His statement was that karate grappling was "crude" and if your goal is defeat a skilled grappler, you should take a grappling art.
Considering that karate was supposedly designed to beat down unskilled people, if your goal is to defeat a skilled striker, you should probably take a different striking art as well.
As for grappling coming out of karate and other sources, I eagerly await the day we see Karate, Aikido,Tai Chi, Hapkido, etc. practitioners entering grappling tournaments and doing well.