when the GPS is enabled, does it drain battery?
If GPS is enabled at an app level it doesn't use more battery unless an app uses GPS. And even if an app uses GPS it can do so in a way that minimizes it's usage and battery drain. For example if Foursquare were to use GPS efficiently it would only fetch your location when you are checking in or looking up places to check in then turn off it's access to the GPS.

Now at a system level enabling GPS might drain the battery a little but that depends on what you have enabled, i.e. Find my iPhone.