Un-Googled Android Experience With CyanogenMod + Amazon App Store?
CyanogenMod, along with most1 other custom ROMs, only include Android code with a few Google parts - all under-the-hood, of course. They do not include apps such as Play Store, Google Now, Gmail, etc. These apps are available as a separate package commonly referred to as GApps2.

So the answer is yes, you may achieve a "de-Googled" experience if you opt not to flash the GApps package.



1 There are some instances that custom ROMs already integrate the Google Apps, but these are rare.

2 Google Apps