The chlorine will very quickly react with bromide in the spa to form bromine, likely nearly all of it before the chlorine reacts with organics (bather waste). You will have some chloramine production if there is bather waste present, but fairly minimal. This assumes that you have enough of a bromide bank to fully consume all the chlorine added, converting bromide to bromine. For example if you only had 20 ppm bromide bank and decided to add 30 ppm of chlorine, you'd end up with 20 ppm bromine, 10 ppm chlorine in the spa. A bromide bank of about 30 ppm is recommended so that even if you accidentally added 30 ppm chlorine, you'd have enough bromide to convert to bromine. Bromine can actually outgas a bit over time as well so your bromide bank may decay slightly between water changes, hence the 30 ppm recommendation. If you ever use a bromine tablet, that will also add some residual bromide to the spa as well.
Long story short, you do not need CYA in your bromine spa.