No, actually I totally understand about it. About 75% of my paid shoots are outdoor on location and I ALWAYS use flash. And if you note where I shoot (Arizona) the sun is always extreme. So I absolutely know about and constantly use HSS. My flashes are set to HSS most of the time. My shutter speeds are almost always faster than the sync.
The point I was making was more about using the BB than it was about using HSS at faster shutters. And that is where I do not have any experience, but I am guessing that shooting through a BB vs not shooting through one at HSS is not going to be a night and day difference when it comes to how much light gets to the subject. I guess it would depend a lot on the circumstance, but i am guessing that the effect would be slight. The OP was more or less asking if he could double his shutter speed from 1/200 to 1/400 if he used a BB. I doubt that would be the case in HSS mode, but then again, I have not used a BB so i don't know for sure. Just seems like not. But it definitely will not work if not in HSS mode at 1/400. And since shutter does not really effect flash it's kind of a silly argument anyway. So the BB on or not is not going to make or brake the use of HSS and a faster or slower shutter. It's just going to get more light to the subject, maybe, from the flash.
OK, now I see where you're coming from. 
But I read the OP's question a little differently than you did. I did not read it as him asking if using a BB would allow him to double his shutter speed. I read it as him asking if he would be able to use the BB at a shutter speed faster than 1/200. 

