Of course a real RAW is most preferable whenever possible, no argument. As an analogy, audio collectors have no patience with mp3s (the audio equivalent of JPEGs) and want not only lossless files (16/44), but hi-res lossless (24/96 or better).
But if you're stuck with an mp3 and nothing else and need to do edits, you'll have to "convert" the mp3 to a WAV/AIFF, do your edits, and keep it there. In that case no lost audio data is being put back, but no further damage is being done. Topaz's AI is attempting to restore some lost data, though of course the argument is whether this is working, and if so, how much.
In the case of Gigapixel AI I have been very impressed. I've done my own tests and have definitely seen the difference.
I agree with Andrew that the main problem with JPEG to RAW is in the product name used ("RAW") instead of "DMG", which would be quite accurate of itself.