Yes, it has every call I make listed, so I can see each number and if there were roaming charges. But I rarely ever use my U.S. phone when I'm out of the country, although it's always turned on. And when I turn it on, it searches for a signal and I see which local network it's picked up. But I have never been charged when it's on but no calls are made or received.
Are you using a regular cell phone or something with a data plan, like a Blackberry? I've heard of crazy roaming charges with data plans, but not with basic cell phones. If it's just a cell phone and you're being charged every time your phone searches for a signal and you travel extensively, you might want to consider switching to another carrier. I'd be spending a fortune if I was charged every time my U.S. phone searched for a network in another country.