It just removes it from the list, doesn't close it. For example, if you start playing music with Pandora, go to the homescreen, bring up the recent apps list, and swipe away Pandora, the music is still playing, so it wasn't closed.
As far as I know, Chrome doesn't stay active for very long if you move away from it. The system might cache the process so that it can restart quickly, but that doesn't mean it's using any battery. You could always do a quick experiment by opening Chrome, then going back to the homescreen, then check Running Apps to see if Chrome shows up. Then see how long it takes for it to disappear from the list.