Actually, if you leave the GPS on, that just means that an app that needs/wants the GPS can use it when you start it. Otherwise, its not doing anything. Although there does seem to be a bug on DX where the GPS will keep the phone from sleeping, even if the screen is locked and the GPS isn't actually doing anything. The 2.2 update is supposed to be fixing that when it comes. I leave the GPS on on my DX, and I get plenty of life out of my battery, going on 13 hours and still have 40% left, even with the bug. Now, if you leave Maps or Navigation or something open, that will eat through the battery pretty quick (still not as quick as on my previous iPhone 3Gs).
By the way, maybe give c:geo a try too. I've heard a lot of people say it's actually better than the official Geocaching app.
Good call.. I love c:geo. Does a great job on my Droid.