It is easy to see the effect of the distortion correction when opening the RAW image file in a converter program that allows for not applying distortion correction. One such example is UFRaw.
Here is an example image. It was taken at f/2.5, ISO 400, 1/13 second exposure. Both the out of camera corrected JPEG, and the non-corrected RAW image are shown below:
It is apparent that there is some barrel distortion in the RAW image. To correct this requires about -14.5 adjustment in the Lens Distortion filter within The Gimp image processing software. This is slightly more than for the Lumix 20mm lens, for which I found that -13.5 was an appropriate adjustment.
This picture shows what sensor area is lost during this conversion: The area outside the white frame is unused when applying the distortion correction.
This corresponds to around 12% of the sensor area, and hence you lose around one megapixel of resolution with the normal 12 megapixel sensor. This is nothing to worry about.
The upside is that if you need a wider field of view, you can use the whole sensor output from the RAW file. The normal diagonal field of view for this lens is 75°. Using the extra sensor area output to the RAW file gives you around 80° field of view. Of course, this will not be distortion corrected, but as long as you don't photograph any straight objects, this shouldn't be any problem. For nature and people, this might not be an issue.
Framing your picture will be difficult, though, since the viewfinder only shows the image after the distortion correction. And you might experience more vignetting in the extreme corners.
Insufficient distortion correction
To my surprise, I noted that the distortion correction is in fact not fully sufficient. After the in camera distortion correction, there is still some residual barrel distortion, especially at shorter focus distances. You can note this in the top left image: The pillar to the left is not entirely straight. Also, the ceiling is slightly distorted.
It could be that newer cameras do a better job of correcting the distortion.