It can.. you mentioned they are koi goldfish mix, which to me says the fish are probably small like you mentioned.. the bb can get caught in its system, a larger koi I probably wouldnt worry as much.. also depends on if its one bb or many.. me personally I would take your sons gun away.. also depending on your water quality its not uncommon to lose a fish during the weather changes.. expecially if you have a severe and quick change.. goldfish I think are more at risk.. I have lost one koi before due to extreme weather changes over just a day or two.. It went from freezing to almost 70 in just a day if I remember correctly.. and it was one of my smaller younger koi..

It is doubtful the fish swallowed the BB. I have seen too many fish mistake something inedible for food and they just spit it out. While it is possible a fish would get something stuck in it's mouth it isn't likely it would happen to more than one. However it is possible for fish to die from a fright. If he managed to hit them with a BB it might scare them sufficiently to cause them to die. The changes in the water as the weather gets warmer can cause fluctuations in the pond chemistry that could kill them. Parasites are particularly active as the water warms up and must be considered. Have you done any water testing? It is important to maintain certain chemical balances in the water and PH in particular can be a problem but it is easy to fix.
How sad your son isn't able to enjoy the exciting things that happen in and around the pond. I would be making sure my kid was participating in pond maintenance. Sandy

Are BBs made of lead? I'm not familiar with fish physiology but certainly dogs that have been shot with buckshot can die from lead poisoning weeks later. And it doesn't take that many pellets, either, to kill a 50 lb. dog.

BB's are copper but there are other ones that are grey that I think are lead..

Lead bbs have been illegal for years. A few major die offs of ducks and geese caused investigations by groups interested in hunting and environment. This lead to discovery of lead poisoning in ducks and geese and in people eating them. Additional studies showed the lead was ingested rather than coming from wounds. The birds were ingesting the shot as they fed from the bottom. It was an accumulation of shot that had missed the birds. Laws were made, waterways dredged at great expense. lead shot no longer made or sold. New deposits show up from time to time.
Sometimes fish do swallow rocks that are too big to swallow and too big to spit out. If it is not noticed and removed the fish could die of starvation or panic. Sandy