I think you could do a fair amount of pass-through and simple processing of audio with an arduino. As you say, 22k samples/second at 16MHz CPU speed gives you something like 700 instructions to "process" each sample. Note that in general, both reading and writing analog data is going to be more than a single instruction, and "real" audio algorithms like digital filtering end up taking a very large number of cycles to implement (and perhaps lots of memory as well), but I bet you could do a pretty good job of (for example) recording audino to a serial flash chip or card, introducing distortion, etc; the sort of things people used to do with simple electronics cleverly used to make guitar effects devices, for example. Compressing the audio using a modern scheme like mp3 is probably out of the question, though.