This reminds me of years ago when I was training in Aikido and one of my dear friends and teachers, Fred Wagstaff, would get a call, "Do you teach monkey-bite kung fu?" His response would be, "Sure! Come on down!" I should adopt Fred's response, but the follow-up question always leads to the crucial issues, "Do you, like, roll around on the ground a lot?" My response is usually, "As little as possible."
Let's face it, any complete martial art has to have three components: striking, grappling, and locking. Black Sword Aikido certainly has a striking component, atemi waza being the heart of Black Sword Aikido, as it was the heart of Ueshiba Aikido. The locks are clear, with the restoration of Aikido joint locks to make them more efficient and the addition of a plethora of Chin Na locks. Black Sword Aikido prefers to grapple in the upright position and to throw and pin. Brazilian Jujitsu prefers to grapple in the supine position. The advantage of grappling in the upright position is that you can deal more effectively with other attackers, and you won't have your head kicked in by one person, as you roll around on the ground with another person. Lastly, it's dirty down there, there's uncomfortable curb stones, broken glass, and dog doo.
Brazilian Jujitsu's preference for supine grappling is obvious, it's Judo! World class Judo, Judo performed by very skilled athletes, but Judo, nevertheless. It troubles me to see how little respect some of its practitioners have for the Japanese and how little they attribute their martial art to their Japanese teachers. I have no problem acknowledging my Japanese and Chinese teachers. Just as Brazilian Jujitsu prefers to grapple in the supine position, you will note that it prefers to lock in a supine position, as well. Judo, once again. If you watch the UFC matches, you will see that the traditional interrelatedness of striking, grappling, and locking remain constant. The defense to striking is grappling. The defense to grappling is locking. The defense to locking is striking.
There are, of course, other problems with Brazilian Jujitsu and the UFC. First, the rules of the UFC prevent biting or eye gouging. This has to be because I doubt many professionals would risk blindness and disfigurement, nor would pay-for-view show it. However, the obvious defense to prevent someone with whom you are rolling around on the ground with from choking you or locking your joints, is to attack the eyes or bite their arm. In a real life confrontation on the street, your attacker may not be so kind as to refrain from this. Secondly, the length of time that it takes to subdue someone by rolling around on the ground with them. And, incidentally, needless to say, rolling around on the ground with someone is a one-on-one confrontation and is useless in defending against more than one attacker. But to return to the time limit, to have as the basis of your system that it may take twenty minutes to overcome your attacker is a great weakness. It would be useless in a battlefield confrontation, useless in a police situation, useless anywhere other than in a pit fight, or a sporting event. You'll notice how integral it is to the system that it is anticipated that it will take a long time to subdue your opponent, that when the time limit was imposed on the UFC, Rorion Gracie stopped fighting and sold his interest. You will note that the rules in the UFC have been changed and now the contestants are permitted to roll around on the ground for only a limited time and then are returned to an upright position. This is because, from a marketing viewpoint, it's boring. This is the same trouble that wrestling had when it was introduced in the first part of the century and wrestling and boxing were equal draws. Boxing caught on because there was action. Wrestling did not because the audience grew bored of watching someone hold another person in a head lock for two hours. Consequently, the only thing left of wrestling as a commercial enterprise today is championship wrestling, which is a demonstration with plenty of action, not a contest.
In any event, the answer is "Yes, we do teach grappling, but not Judo grappling." This makes sense because we're Black Sword Aikido, not Judo.