If the microphones, ADCs etc on both phones are incapable of capturing frequencies of above e.g. 15Khz below a certain range, combining those signals definitely won't bring you any closer to the original signal. You may be able to cancel out a fair bit of noise given enough processing but you won't get back what hasn't been originally captured by either device.
That's before you get into phase problems from trying to combine two signals. A likely outcome is that the amplitude of some signals are increased whilst some are decreased due to phasing issues.
/fuzzily remembered music tech degree. May be too fuzzy though!
Isn't downvoting for removing bad content, not trying to silence someone you don't agree with?
Thoughts/comments?
(edit - post is no longer showing as greyed out/downvoted - but still, any comments?)
The more challenging problem is the distortion from the phones being overloaded, crowd noise, built in limiters, different sample rates and compression. It is true that phase relationships from a single sound captured by multple sources can be very problematic.
However, the further the mics are away from the source the less this a problem at least with "phaseyness." This annoying artifact is a type of comb filtering , and it's based on the fact that two mics close to a sound source can be thought of really capturing the "same" sound at slightly different times. If the mics are far apart, the sound is no longer the same: it's picking up reflections from a myriad of sources, the phase relationships within the frequency spectrum have been smeared and shifted by traveling through air. This negates a lot of phase problems. The more likely problem is cancellation in the low frequencies which can be ameliorated with time alignment.
Chances are that there is a low pass filter in front of the phone's ADC, blocking signals above the Nyquist limit from reaching the sampler. Assuming brick wall filters (ie perfect cutoff), combining the signals will reduce variance (noise) but not give any information on frequencies above the cutoff frequency of the filter.
Brick wall filters don't exist though. What you might see is a miniscule amount of signal in the filter's stop band. Combining the signal from many many phones might reduce the variable enough to give useful information for frequencies a tiny bit above the cutoff frequency.
A cool project would be to gather the audio from every networked microphone in an area (mobile phones, laptops, ...) and use beam-forming techniques to reconstruct the sound pressure field as a function of position. My guess is that the system would be sensitive enough that it could do amazing things like capture conversations though walls or from long distances.
I think this is technically not quite true. If two cell phones right next to each other are both sampling at 15kHz, in the best case you could combine their samples to get an equivalent sampling of 30 kHz. (Best case meaning phone 1 samples exactly half way between phone 2's samples.)
In practice, however, you would have to account for positioning and the fact that the phones' samples aren't perfectly offset from one another. It would require an amazing engineering feat to overcome this challenge, but I think it's within the realm of physically possible.