Is it conceivable that these two reagents would react with each other? what experimental evidence do you have to support your answer?

Under controlled conditions, sodium bromide and hydrogen peroxide are actually able to react. However in this experiment, I do not believe that they would react. This is due to the presence of other compounds which are used in the reaction and the means by which the compounds were added to the solution. There are actually a few clues that can tell us whether they are reacting. The most obvious one is that there would be bubbling due to production of H2 gas.