Is it advisable to occasionally put some chlorine bleach (sodium hypochlorite) into the brine before a regeneration to clean and disinfect the resin? This would be in the context of non-chlorinated water, in my case behind a granulated carbon filter.
I agree with Tom that chlorine is not good for resins due to its chemical compound and the resins reaction to contact with it. Resins will swell with chlorine. Eventually, they will become 'mushy' and start to deteriorate needing replacement due to lack of effectiveness.
However, a sanitization of resin by placing an adequate amount of unscented bleach in the brine tank may be the better of two evils--the other being bacterial colonization and any accompanying odors.
The key differences in having a softener on chlorinated city water and that of a very occasional sanitization is duration and concentration. On city water, the resins are in constant contact with lower levels (0.2 - 0.6ppm) over a very long period of time---years. This long-term saturation (service, brining, backwash and idle time) will cause resin to lose their effectiveness. There will be virtually no chance of bacterial growth so sanitization is never needed.
With sanitization on well-water applications, the resins come into contact with much higher levels of chlorine but for a very short time and only during the brining stages, after which it will thoroughly rinsed away leaving the resin chlorine free. There will be a given, much lesser, amount of chlorine remaining in the brine tank to be applied during the next brining stage. This short time of chlorination, done sparingly, will not have a greatly negative effect on the resins and certainly not as much as that on city water services without carbon pre-filtration. Its benefits may greatly outweigh the detriments if done properly and only when needed.
Resins are actually very tough and can withstand a great deal of punishment.