To be honest I don't think there's any benefit to doing it that way compared to going straight from low bitrate mp3 to high-bitrate mp3. Most audio conversion programs uncompress the mp3 anyway, as part of the conversion process, as a temp file.
I should stress even in my experiment, there was only a small, albiet noticable, change in quality, but what The_Other_One said is right, when you start with a poor quality raw material, you're basically stuck with it. I think what increasing the bitrate does is analagous to using a smart resize on an image, by creating averaged inbetween pixels. It may look better than increasing pixel size, but you are still left with a poor quality image.