Yes, it is possible to have a CBB with tang(s), but it dosen't necessarily make life any easier for the CBB's (which are delicate and need the easiest life we can offer to them IMO).
My CBB is with a chevron tang now. For it's first 1.25-1.5 yrs with me, it was housed with a powder blue, when the CBB finally started taking mysis, it also took on a a new bosteriousness, it would actually push the PBT around! I'm not kidding, the CBB was boss of the tank then with the PBT, and just as much now with the Chevron (which is a much milder manered tang than the PBT). I think I and the CBB got lucky more than that it was ok to house the CBB with the PBT. Looking back, maybe I wouldn't have had to feed little necks for all that time if the CBB hadn't been intimidated by the PBT for a long time? Also, keeping in mind that all fish sp have variable personality traits, well, I suspect that my CBB was born with the fish equivilent of a Navy Seal type personality. Sort of like that one in a million Deer that charges you instead of running away. It thinks it's a real tough guy, but this is not at all normal for a CBB..
Personally I strongly agree that the active swimming and somewhat intimidating/intrusive styles of all the tangs I've kept, IS a stressor to any gentler fish such as a CBB. Add that to the fact that CBB's can be very deilcate and hard to get established, it's not a good mix IMO.
Awsome fish, but not one to try without some serious planning and willingness to go out of your way to keep happy. (starting this thread is a great step in the right direction..)