without much sound quality loss?
Well, that depends on "the rest of the circuit." 10 bits of ADC gives you an error (theoretically) of about 0.1%; are you using a 10bit DAC as well? 0.1% resistors? Components in general designed to have 0.1% accuracy over the operating range (power, temperature, etc)? Silly expensive microphones and speakers? Trying to build an A-D circuit that was actually accurate to 22 bits would scare the crap out of me...
The ADC you reference doesn't "sample" fast enough to do audio (10 Hz for 20bits) You'd be MUCH better off with the internal 10bit ADC if you want to do audio. "CD Quality" is 16bits at 44.1kHz sampling. The Adafruit "WaveShield" has a 12bit DAC doing 22kHz, and I'd describe it as "pretty good" (probably as good as recording sound on a cassette tape, and better than most microphones.)