The push for copper bullets is biggest in the west where condors range. The endangered California condors. I cannot find the paper - it is more than 15 years old - where a couple of veterinarians got in on a cull deer hunt. They ex-rayed the carcass and found lead fragments, The gutted the deer and found fragments in the gut pile and in the carcass that were invisible to the naked eye. All lead bullets left an exit wound in the critters. Unfortunately, condors are very sensitive to lead - and there was enuf in a gut pile or in an unrecovered critter to poison them. When gps-collared condors stop moving, they go out and pick them up, remove the lead from their system and return them to the field. Bald eagles are also susceptible to lead poisoning and the timing is consistent with deer hunts creating gut piles. This is becoming an issue in at least half a dozen states. Some eagles are rehabbed, some are put down, and many are not found. the ONLY weak link in this science is that one cannot say the lead from hunter A's bullet caused the poisoning in eagle B.
Copper bullet performance on game is outstanding; I hve taken more than 20 animals with Barnes bullets. Antelope, deer, elk and even a bison. Recovered only 2 bullets, both muzzle loader bullets from bull elk Once you switch you won't go back
To the original posters question: the lead from your shooting will not likely have a detrimental effect unless the lead gets eaten somehow, most likely in a carcass. A bullet trap removes any doubt.