Good idea. When I worked as a vet nurse, we got endless injured birds or chicks in. Those we could, were sent to a wildlife centre - but the majority were actually PTS. Simply because we could not spend the time and money (we were not a charity) to help these animals. And the wildlife centres weren't that close and they just simply were not willing and able to do daily trips to use - we always had to get there birds there in our own time and cost. I personally took on what I could and between the staff we always tried to do the best we could - but there were just never enough people.
So once you find out if you need any special licenses etc. to keep / help / rehabilitate these wild birds, I'd say you should also make yourself known to some local veterinary practices. We were always looking for people like you.