That's true for a lot of products with Audyssey, but not all. And it has nothing to do with Audyssey itself. Audyssey processing is ALWAYS done in the digital domain (PCM audio format). Most AVRs and many surround processors only have a single stereo ADC chip (as opposed to DACs). ADC is Analog-to-Digital converter... this chip is required to digitize analog audio inputs. If the product in question only has a single ADC, you can only process analog audio through Audyssey if the analog audio is in stereo. However, there are SOME processors and AVRs with 8 or 10 channels of analog-to-digital (ADC) conversion and those will process multi-channel analog audio through Audyssey if you want to do that. There is an inevitable audio quality loss when you convert analog audio to digital (current ADC chips are better than ever, but still seem to not be quite as good as what they do as today's DAC chips are at what they do). So you have to decide if converting a high quality analog to digital so you can get Audyssey processing is worth the small ding in ultimate audio quality in order to benefit from what Audyssey does to fix room-related issues.
The audio ADC chips I'm familiar with that would be used in conjunction with better DAC chips have comparable SNR and SINAD specs from 110 dB to mid 120s dB. So you're talking about adding something on the order of one to 10 parts per million of noise/distortion for one pass through an ADC/DAC tandem. God bless you if you can hear that difference.
On the other hand, if you suppress a 10 dB peak in the LF frequency response due to a room mode by using Audyssey, that will be very audible.