Before I begin, let me just state that I am aware of these facts:
1) Lossy to lossy encoding in general is best avoided, if possible. 2) Encoding to a higher bitrate won't result in a file that is better than the original. 3) All encoders are not created equally.
With that said, here is my question. When one must re-encode a lossy audio file (such as MP3), in terms of audio quality alone (file is is not important), will re-encoding it to a higher bitrate result in better quality audio? For simplicity's sake, lets say I am using the same encoder of the original file. If I have a 256kbps MP3 file, re-encode it to 320kbps MP3 (using identical encoder), will the audio quality be better than if I were to just re-encode it to 256kbps MP3?
What got me thinking of this in the first place is when I was producing MP4 video. I added a few songs to some of my videos, most lossy MP3 and AAC of around 256-320kbps. When encoding my project to MP4, an audio bitrate must be selected. The highest setting is 384kbps AAC. File size is not important, I just want the highest quality audio. However I don't want to encode at a higher bitrate than the original if there won't be any difference, or it results in digital artifacts.
It wont relay make a difference. If you want to, make a few different encodings and try blind testing. If you realy want to make it better, you could try remastering it. Here's a guide for Audacity.
It would only make a difference if you were encoding to a less efficient format (eg flac to mp3). You wont get any more sounds that were not their originally. You can only prevent the loss/distortion of more sounds.
Also make sure your audio is compatible with mp4 (when putting it in a video). It depends on the software, but you want to transcode as little as possible to prevent data loss. If the file is already compatible then it might (I said might) just use the original file. Here's info on that.
You already answered your question yourself. Look at fact number 2).
The common approach would be to simply mux (multiplex) the plain exported videostream with the unaltered audiostream if you don't have to edit the latter whatsoever.
As I am yet to find a definitive answer, I formulated a little experiment to test the theory out.
I transcoded a 128kbps CBR MP3 50 times, using two settings. The first setting I used was the same as the original, 128kbps CBR MP3. The second setting I used was 320kbps CBR MP3. The program used was iTunes.
I have uploaded both tracks. As you can clearly hear, the 320kbps version is much better quality. So it would seem that upping the bitrate to higher than the original does indeed preserve more of the data.
I may repeat this experiment again, just to factor out human error.
If you have any questions, please feel free to ask.