no there was no band on the Britannic because she was commissioned as a world war 1 hospital ship if she was used for a cruise ship like what she built for than she would have had a band
Given Olympic's experience, Britannic would likely have been used for cruises from time to time, but neither of them was ever called a "cruise ship." That's a modern term, used to describe ships built for a different purpose than early 20th century ocean liners.