There are two separate 'bits' to locating itself.
GPS has what is called a 'cold boot'. This is when you power it up, it starts listening, and doesn't hear any of the satellites it expects. This happens when the unit hasn't been switched on before (first boot), or has been off for a long time (several weeks), or you have moved a long way (say over 500miles). When this happens, the GPS has to load from the satellites the 'almanac'. This is the data saying what satellites should be visible at a particular time. Now the almanac takes just over 12 minutes to broadcast. However the broadcast is 'overlapped', so if you are seeing eight satellites and they just happen to each be broadcasting 1/8th of the almanac out of sync with each other, you could get the entire almanac in about 1.5 minutes. Conversely the ones in the sky might all be broadcasting the same part of the almanac, and then you get interference just as part is sent, so have to wait for a second time 'round'. So acquiring the almanac, can take anything from perhaps a couple of minutes up to 20 minutes (though with modern receivers that latter is rare).
However, once you have the almanac, if you power up again, even if you have moved, provided it doesn't change the view of the sky very much, you can do a 'warm boot', which takes only a few seconds.
As examples, using an aviation GPS, at a local airfield, powered it up for the first time and it took just on five minutes to get a 'good fix'. Flew 100 miles with it off, and it powered up in under 10 seconds. Then took it over 500 miles _to the east_, and it took over two minutes to get a good fix.
Now key underline on the direction. If you look at the shape of the satellite orbits, moving north/south affects the pattern of them less than going east/west. This is why you will find reference to the units needing to do a cold boot 'if you cross a timezone'.
Now if your change in position was only (say) 40 miles, then it won't affect the boot up speed at all, and if used only a day or two before, the unit will probably have a working lock, before the rest of the system has finished waking up.
This is presumably why you did not see the long delay at your new location.
If the almanac is 99% right, then the the unit will start by listening for a time, then for the satellites it expects. Position within perhaps 50feet, will take less than a couple of seconds, and once WAAS is received, this will drop to only a few feet. The latter is why accuracy of hold etc.., will improve once the unit has been on for a few minutes.
Once you arm, and then advance the throttle to take off, the current position is recorded as 'home'. Even if you were flying only 100' away, and never switched off or removed the battery, it'll be re-recorded when 'take off' is performed.
Since the GPS lock will commonly improve once the copter is airborne, if you are going to fly a distance away, and want to be sure of a good return, re-recording the home location in the air, can help.
The battery doesn't really have anything to do with 'home', except if you have removed it, then you will definately have to take off again, so it will then be re-recorded.
Best Wishes
