There's yeast, but if there's no fermentables left then no fermentation will occur. If you racked before fermentation was finished, then you can have fermentation in the secondary, yes.
Do you think that the act of putting your beer into another container causes the sediment to fall out faster? Why can't it all fall out in primary if you leave it longer as opposed to having it fall out in secondary?
If you primary for a week and then rack to secondary, sure you'll get quite a bit of sediment falling out. If you rack it to secondary after a month, you won't. That's because it already fell out in primary. That's what people are getting at when they talk about a secondary not being necessary.
If you do secondary (and I do) you should wait until fermentation is done before doing it if you follow the long primary theory.