Will cyanide substitute bromine in bromobenzene?
Economically, your approach is probably a bad idea.

But in general, the conversion of aryl halides to aryl nitriles does work.

I have prepared large amounts of 2,3,5,6-tetramethylterephthalonitrile from 1,2,4,5-tetramethylbenzene in a two-step procedure


iodination
reaction of the diiodide with $\ce{CuCN}$ 


back in the days for my PhD thesis. For the cyanation, I followed the procedure described in Synthesis, 1974, 53-55, but used N, N-dimethylformamide (DMF) as a solvent.

The halogen-cyanide exchange is know as the Rosenmund-von Braun reaction and you might find further information in a review on Cyanation of aromatic halides (Chem. Rev., 1987, 87, 779-794).