This would probably have been better posted in the Video Topics forum - I expect those guys would have better answers for you in this instance!
I don't think Vegas can save the AVI without rendering the video again. I suspect there may be tools out there which will let you merge an audio file to an existing Video file - but I don't know if they can skip the Video render either.
You'd have to open the original AVI in Vegas, edit the audio, render the audio as a WAV file and finally use a 3rd party tool to combine the WAV and AVI video file. This assumes that the original audio can be stripped out by the same app.
If your source AVI files is either uncompressed or strict DV format, then the video won't be re-rendered if you save to the same format. The frames will be copied bit for bit to the new file. Re-rendering is only necessary if going between other compressed formats or if any changes are made to the video track.