As an audio enthusiast and programmer (not an expert), I would categorize this as "possible" with a big footnote. You'd most likely be improving fidelity rather than restoring, and you'd be working via some type of interpolation.
It's very similar to working with picture files. You can't really add resolution, though you can increase the image size, blur the edges and/or run a program plug-in "Fractal Designer" that utilizes algorithm generate synthesized resolution.
In either event, the results would be highly subjective with a variety of options.
For a good idea of what's possible, consider the DFX Plug-in for various players (
http://www.fxsound.com/dfx/index.php ). It can dramatically improve the sound of MP3's during playback, but there are tons of variables and possible settings.
Without the existence of a tool specifically designed to rip with improved fidelity, you might be able to move directly from theory to practice by playing a file back via WinAmp with DFX turned on. You could capture the improved audio stream and direct it to a Wave File, then you could rip the wav to an MP3.
I'd never thought of it until you mentioned it, but the idea seems to make sense.
I wonder if someone has or why someone (including FXSound) hasn't created a ripper/encoder/plugin to take advantage of this.
Perhaps most folks who care about audio quality either rerip from the source or use a own combination of plugins (like the dbpoweramp PowerPack) to make individual adjustments to EQ, Stereo Stretching, Smoothing, and such. They may have ways to achieve the same results by combining various effects.
Still, I think it would make sense for someone to "idiot-proof" the refinement process with some simple controls like DFX. It's an interesting idea. Maybe somebody is doing it. (?)