In general, no. There is a setting however when you first launch the game that will turn off gore. But you know its a cold war era bad ass shooter. Most kids are probably into the multiplayer not the single player. Its a way for them to "prove" who's skilled and better.
Looking at the reviews, Call of Duty: Black Ops is appropriate for kids who are 12 and older. Parents and educators reviewed the game and felt it would be inappropriate for anyone under the age of 12. If really comes down to what your parents think.
In my opinion, no. Black Ops is rated Mature for a reason. It's has some of the most brutal violence I have ever seen in a game. A 12 yr old doesn't need to see that. But it's really up to the parent to decide.
Lol I'm almost sixteen and I have played the halo game when it first came out when I was in kinder. Usually kids at younger ages don't take much offense to the game, but when they become competitive, they will get pissed and start cussing. One thing to remember ;)