You don't have to wait for the chlorine to drop, but you do need to establish a bromine reserve, then activate the bromine with chlorine or MPS before relying on the floater. You may want to look around the rhtubs.com site, and/or the Taylor book if you have one, for articles that explain a bromine system more fully.
Bromine is a lower pH product, and is also more effective at high pH than chlorine, so it may fit your situation well, but as HTDan said, you still need to balance your water. You want to make sure you have your pH/TA/Hardness in line to prevent scaling or corrosion issues, but you can run at the upper ends of the ranges, instead needing to keep the pH low to maximize sanitizer efficiency. Be aware that the low pH of the bromine will eventually erode your TA, then pH, so monitor them weekly and adjust as necessary.
Most bromine tabs have a high % of chlorine in them. The chlorine serves as an "activator", but as it gasses off, it may cause LT damage to the cover and headrests. One option to limit that is to use the Brilliance brand of bromine tablets, which do not contain chlorine. You will need to add chlorine or MPS doses separately to activate the bromine, but can do that with the cover off to minimize offgassing damage.