Would the Arduino be fast enough to process 6 incoming signals and determine the frequency of each string
YES! I can tell you it IS POSSIBLE to use an Arduino (with support circuitry) to convert every note/fret/string (even CHORDS!) that is plucked/slide/strummed in an standard electric guitar to MIDI notes.
I've seen it in action, I've heard it.
An engineer friend of mine did it. Of course, it's not just an Arduino, there are other circuits required/involved.
I can't offer any details here (I'm on NDA), other than say the Arduino/AVR chip is more than capable for this task.
... you guys need to stop looking at this problem like a true blooded engineer (from the sound of your questions, re: how to sense 6 signals, determining freq. of each string, etc). You also need to look at this from a guitar player's point of view - that's the key to solving this! A guitar player doesn't think, "I need to play this frequency" right? He doesn't even think that way!
The whole point of this project is to detect finger positions, even when no actual notes are being played.
You're getting warm.
That's why I said the question how to detect. freq. of each string is unneccesary)... that's not the key to solving this problem. Think like a guitar player. Ask someone who knows how to play a guitar, or learn how to play a guitar. And oh yeah, don't go into the deep end with Fourier Transforms and all that shit. Think basic electronics... what's the first formula you learned?