If you're using an icon that looks like a swastika in Call of Duty: Black Ops, you will be banned from Xbox Live. Director of policy and enforcement for Microsoft's online service, Stephen Toulouse, made that clear a couple of days ago on his own blog after telling a BLOPS player via Twitter the very same thing.
The reason you'll get banned, of course, is that the swastika is a sign of monstrous hatred, violence, and abuse. No one needs to be exposed to the distasteful symbol when they're just trying to fit in a couple of games of BLOPs on a Monday afternoon.
Toulouse lays this all out well on his blog, while also admitting that not all usages of the symbol through the ages have been in the same spirit as the Nazi party in World War II. In fact, the post as a whole serves as a huge rebuttal to those who are somehow mustering up arguments against these possible bans. What's important to remember here, regardless of how you feel on this, is that Xbox Live is a private service and Microsoft can regulate content on it however it sees fit. It could, theoretically, ban the word "Brad."
Summing up the stance in Toulouse's words:
The Xbox Live profile and in-game content you create is accessible by everyone. You do not have the context inside of it to explain your long-winded contrarian view that your pithy text that violates the Terms of Use or Code of Conduct is actually intended to change people's minds about a commonly held understanding.
It's not political correctness, it's fundamental respect. If you think the swastika symbol should be re-evaluated by societies all over the Earth, I think that's great. Your Xbox Live profile or in-game logo, which doesn't have the context to explain your goal, is not the right place to do that. And by the way, that doesn't just go for the swastika, it applies to many other symbols as well that my team does indeed take action on when we see it.
If you're wondering how a player could even use a swastika icon in BLOPs, look no further than the game's robust icon creation functionality, which like Forza, allows you to take pre-existing images and layer them on top of each other. With enough work and cash earned by playing the game, you can create a symbol widely recognized as a hateful and hurtful one and then display it for others in matchmaking lobbies or even on your guns. You can also make phalluses or create pictures of unicorns banging bears, both of which will also get you banned. You have been warned!