No, you should not just run above someone's head and report them to management over a body odor problem out of the blue. Not only is that a very unfair thing to do to your co-worker, but it is going to negatively effect your working relationship. If it's as big of a problem as you seem to think it is, management will get a whiff of it themselves. If not, then you shouldn't be the person throwing everyone in the office under the bus in order to build your own cozy little work environment. It's just such a petty thing to go around getting co-workers in trouble for.

Frankly, BO is a rough thing in China--maybe this is different where other people are, but in my city, there's not a stick of deodorant to be found. Thankfully, not a problem for me--showering regularly does the trick. Other's didn't luck out with the body chemistry thing...it's not their fault.