Everyone is born to sing. The problem is that we forget as we grow older. The process of learning to sing is the process of rediscovering your natural abilities, and then training them.
So the answer is yes, you have to train it up like an instrument, and anyone is capable of doing that. But there's also those few people who kept their ability to sing from childhood, and they don't need so much training as the rest.
Either way, training will improve your skill. Even the best singers are constantly training their voices to higher levels.