Use copper wire to prevent moss growth on a roof

In a way it does. It's a lot like Rain-X makes water bead up on glass, masonry sealant will make the water tend to bead up and run off of brick and concrete. However, much like Rain-X, it wears out every once in a while -- probably more often in the PNW where it'll get wet all the time.

The moss grows because there's easy moisture to be found within and on top of the brick. However, the sealant won't prevent moisture that's deposited on the brick by fog / mist or dew from collecting -- all three things are common in the PNW due to the relatively high humidity. Therefore, it'll help a bit, but it's not a total or even ideal solution.

Although -- the Thompson's sealant is not the best on the market by far. Look at the Behr stuff.

The bleach mix will be dilute enough that it will not be of harm. I've used it myself at least a few times to kill off algae that has accumulated.

You can also use things like Oxy-Boost and Stain Solver, a bleach substitute which I believe contains some hydrogen peroxide. It will also work against light moss and algae, yet perhaps be less harmful to plant life underneath.

More importantly is to fix the source of the moss. Roofs that gather moss tend to be too shaded, under big trees that stop it from drying out. You may need to open things up, just by a bit, but enough to let it dry out. Yes, those trees are a natural source of air conditioning, but trees tend to grow. So trim off branches that overhang the roof. Cut a few others out to let the sun in.

For roofs that have only a bit of green, you may find it is sufficient to add zinc strips along the top. The zinc leaches out, keeping the roof clean of moss accumulation. There are also shingles with a moss inhibiting additive that prevents moss from growing. Copper strips should also work, and copper flashing is easily available. I've even read that you can glue (use silicone) copper pennies just under the edge of the top row of shingles. They are mainly zinc anyway.

If the moss had accumulated heavily, the problem is your roof likely needs repair, as it will have been too wet for too long. The shingles will need to be stripped off and replaced, but probably the roof decking will be soft and need some repair too. This can best be judged by a professional who will inspect the roof carefully.