This is one of the biggest questions asked, and it appears many roof companies have different opinions. Mark Poole from Waterworksnw made this statement on his blog:

"Many roof moss removal companies will encourage you the client to remove the damaging moss right away. But are they doing more harm than good by removing live moss from the composition roof material before it’s even been treated. Many companies offer roof moss removal, and same day service! The problem is when you remove live moss from the roofing material you not only are creating wear on the material, but you are creating new breeding ground for moss spores. Particularly in the Northwest moss is always going to try and grow on roofing material, we know this. By treating the moss first, you will loosen the mosses grip on the shingle material making it easier for roof moss removal if needed. Also treatment goes down to the root structure, whereas pressure washing or brushing does not.

This is not necessarily true, considering he just got his moss treatment license and he doesn't do the work himself. It is possible to get a nice clean slate with little wear on the roof. What my company does is use a medium strengthen plastic broom to room the heads of the moss, (the big chucks) leaving the "roots". Then with a garden hose and a fine tip we can trim our each shingle which does two things, removes most 80-90 percent of the roots, and rinses away the environment moss loves, which is a little soil, dirt. The PSI from the hose is no more than 50 PSI which is about a hard rain we receive from living in The Pacific NW. This cleans up really nice and we then can treat the roof, which will get a straight shot to the remaining roots and roof structure, and it is biodegradable, unlike the powder that is used by WaterworksNW and others. Also powder is really marginal with effectiveness on many roofs without making the roof look like a bad looking partially white decorated roof. And if the customer wants we can come back to remove the rest, the product we use dries up the moss really small because we already removed 80-90 percent of it.

And just powder treatment alone does not get rid of the moss. It also may not kill the large chucks (anything thicker than 1 inch), so a company will have to remove at least part of it before treating, than remove the dead if any, after it is killed.