This is a somewhat controversial topic. Clearly, one should not pour acid into the skimmer. Adding a chemical like baking soda into the skimmer slowly enough to not clump up is clearly OK. Pouring chlorinating liquid or bleach into the skimmer infrequently isn't a problem, but the question is whether regular addition has any effect on pump seals or other equipment. In my own pool, I try to open the cover and pour slowly over a return flow at the deep end, but in a pinch infrequently I pour into the skimmer if the cover is a mess, for example (I have to clear it off before opening it).
There are quite a few people who pour into the skimmer and haven't reported problems. I'm just concerned because the chlorine level is clearly higher, but the high pH moderates that somewhat and the exposure time is relatively short.