Ok, here's the useful answer

Firstly, let us assume that we can somehow get the guitars output into the empeg using the line input. It might take a small preamp gadget, but it's doable.

Ok, that leaves the challenge to be:
1) Tell the kernel that we want to sample the input. In practice, that means to make the same ioctl calls to the kernel that the player makes when switching to aux in. We know that 'Aux In' visuals have to be sampled somewhere...
2) Read the samples into the application. The sample rate is not an issue - ISTR that the sampling rate is 22.05KHz. Obviously the root frequencies of a guitars strings are a couple of magnitudes lower than this, so Nyquist can piss off and mind his own business.
3) Do a fourier transform on the samples. This is the tricky part, but obviously doable since many of the players visuals rely on such transforms. Aside from the fact that coding fourier transforms isn't particulary trivial to begin with, we also need to remember that musical notes in the lower octaves aren't integer Hz, and the fourier transform needs to be able to measure this. (I doubt the player FFT code cares about that point).
4) Find the highest peak. Sanity check that it's also the lowest frequency peak and that we're not getting a harmonic at a higher level than the root.
5) Compare the frequency of that peak to an array of frequency ranges to find out which note it is closest to.
6) Display the note, and an indication of which way we need to tune to get absolute.

There is another approach that might have some merit investigating;
Instead of measuring the current tuning of the string, we could use the DSPs tone generators to play a note that we could tune against. This would avoid the hassle of coding FFTs, or dealing with guitar signal levels. In fact, the userland coding would be trivial.
I'm in the process of developing arbitrary sine wave functionality along with appropriate userland ioctls anyway, so once I've gotten that stable and accepted into hijack, it would just be the case of using a look up table to find the appropriate frequency for the note in question, and then call the ioctl with it.
The limitation of this approach is that the DSP can only play integer frequencies, so low octave notes are going to have errors in them. But we could tune using harmonics, a technique that many guitarists use when relative-tuning anyway. And we should be able to hear beat frequencies.