There can be multiple answers for the same question on Denon/Marantz's Eco settings, if the question does not provided the needed specifics. A definitive answer can be given if the specifics need are provided.
Examples:
1) Would Eco "On" affect sound quality?
Possible answers would include but not limited to: Yes, No, Depends,.........
2) Would Eco "On" help keep the AVR run cooler than Eco "Off"?
Definitive answer: Yes
3) Would Eco "On" affect sound quality if I sit 8 ft from my Klipsch speakers (8 ohms) that has sensitivity bench test measured 93 dB/2.83V/1m and I don't listen loud, may be 20 dB below reference level at the most?
Answer: It depends, if you listen to music and movies that don't have much dynamic range, you may not noticed any degradation, otherwise you may, during the peaks in the music/movie contents.
4) Would Eco "auto" affect sound quality if my volume setting is always higher than -25?
Definitive answer: No, because with Eco in "auto", it will stay "Off" at volume position -25 and would never turn "On". It also mean it won't help your AVR stay cooler.
5) Would Eco "auto" affect sound quality if my volume setting is always lower than -30?
Basically the same answer as for 3) above.
6) Would Eco "On" affect sound quality if I seat 10 ft from my speakers that have sensitivities between 88 to 90 dB/2.83V/1m and I listen to 5 dB below reference level?
Definitive answer: Yes, there would be degradation due to limited output
So you can see that there could be a lot of possible responses for a lot of scenarios, and the examples I used above may not be 100% correct, as I have had only one coffee very early this morning.