I can only provide my experience
will a relatively inexpensive streamer played through a decent DAC give CD quality results? Already being a Amazon Prime customer is their streaming service on par with the other variants.
Depending on what is perceived as decent. I’m currently using the PSAudio MK1 as a Dac. I think it’s decent but YMMV
I’m don’t currently have my CD player hooked up but I can compare converted flac files to streaming.
I’m using a Windows Fanless PC using Foobar 2000 for streaming flac files compared to Amazon Pirime with USB output to the DAC. Local files sound better... not a lot better but better. I’ve used Qobuz in the past and it sounded better than Amazon Prime but still not as good local files.
(I also have a PI2AES streamer on the same system) local files both I2S and AES/EBU sound better than the fanless PC but sadly can’t provide Amazon access which is why I have both streamers.
The final note is that the sound difference from best to worst is a matter of several degrees. I would not be able to tell which configuration was playing if I wasn’t able to compare them directly.
So my answer to your question is No you will not get CD quality using Amazon and other services like Qobuz. While Qobuz does sound marginally better Amazon can still sound pretty darn good.