Absolutely bleach the exterior surfaces. There are a few things to remember.
First, something I learned from Bill Nye the science guy. Too much bleach is not better. We use a 1-4 mixture.
Second, be sure to get the mixture off any glass surfaces reasonably quickly. Try to not wash on the sunny side of the house as the salts in the mixture will etch the glass if left on to dry.
Third, rinse any delicate plants both before and after applying the mixture.
Fourth, use care bleaching near copper and brass items as the mixture will cause these surfaces to turn and tarnish. Rinse well with clear water before and after applying the mixture.
Finally, be sure to rinse all surfaces following the bleaching, as the aforementioned salts will leave a residue. This, or any other contaminant is subject to cause adhesion difficulties for any coating.