Eldar14 provided a good example with the dogs and lions (even if a comparison with a wolf might be closer to the elf/human vs orc relationship). But one thing is missing. There are lion cubs, or wolf cubs, that are raised by animalkeepers and I've seen lion behave like peaceful kittens. They have a inherent nature for violence, yes, but they can control it. And there are dogs that bite their owners, just like there are elves and men that turn more or less evil. Yes, elves too make stupid things that hurt their own.
I won't tell you that raising an orc baby as your own won't lead to complications. The violent nature and misery of their race is probable partly genetic, but with the right upbringing where morale and normal values are a part of their life, even orcs can be turned into something functional in the "good" society. To pick a fight with one of these orphan-orcs may not be a very good idea, but if they're kept away from things that will trigger their instincts, I think they deserve the chance.
To say that Orcs are irreversible evil and forever lost doesn't fit very well with the view of a forgiving God that most Christians have. See also the quote
Son of Númenor provided; Orcs are not irredeemably bad.
Fact is nurture has such a big impact on an organism that it would be strange if an Orc couldn't adapt itself to society. Not even clones or identical twins behave identical. For example: cows with the exact same genetic material take on different roles in a group. The first cloned cat (Copy Cat

) was a copy of it's mother, but it's personality was different.
If an orpanaged orc would be happy is another question. To know what "it" is and carry with it the "misery of it's race" and inherited hate could be to much to bear...