As with most chemicals, it depends on the concentration.Chlorine is quite aggressive. It's entirely possible it will destroy the mechanism you proposed, although I'm not speaking from experience.
I would not go blindly dumping gallons of bleach down the well. If you can measure the well depth, and depth to water table you can calculate out the volume in the casing and adjust you dosage to achieve a total cl2 of around 2-3mg/l then look for a free chlorine residual of 1mg/l after 24 hours dependent on the TOC levels (total organic compounds) These levels would be perfectly safe for the plumbing components however multiple treatments may be required before achieving the 1mg/l free chlorine after 24 hours if the demand is high.
Shocking the well (super chlorinating) with about 12 to 15 mg/l cl2 with clear things up a bit quicker but is harder on components.
Think I remember reading that 3% bleach can dissolve brass a a rate of up to .010" per hour while giving off a toxic gas. (have to look up what the gas was but it is listed on the SDS if your really interested)