Does the GPS hardware draw power when no app is using it? That is to say, does the hardware itself do any periodic updating/searching for satellites, etc, if there an no running apps which require GPS information?

If so, what sort of effect does it have on battery life?
Most phones tend to cache your location periodically and use this information when requested by you applications so that battery drain isn't a big problem. 

I believe this is called assisted GPS. 

This does have the disadvantage of allowing to your location to quickly become inaccurate. Imagine if your location is cached as you get onto a train,  you then you take a photo at the next platform, but your location wasn't updated, the location stored in the image could be miles out.