Then you're removing more information recording the analog output of your soundcard and adding whatever shading or quirks lie in its circuitry or electrical interference resides in your computer case
There is no analogue circuitry in play here. Audacity will record the digital output from the soundcard of what (I assume iTunes) is playing.
So that's exactly the same quality as the original m4p file.
Then if you save that to a lossless format, e.g. as flac, the sound quality of that flac file will be exactly identical to the m4p source.
Also, as the OP stated not being 'an audiophile'; if the m4p is of a good quality/high bit-rate to begin with, even when trans-coding it to mp3, many people will not be able to notice (or care much about) the regression of sound quality.
I myself have been called an audiophile, and I have tested transcoding some good quality lossy files to lossy.
Partly because I was taught you should "never do that!", and the rebel in me said, do it!
And after testing it, I must admit I was surprised that for certain types of music/recordings it was not that easy for me to notice the added regression of sound quality.
So I am guessing the OP wouldn't need to worry that much about this.