This isn't really Android without Google - if you do this, you're still using Google's services and piping data through them. It's kind of like switching from Chrome to Firefox to open Gmail.
RTM. From the article:
"If you read the purpose of microG you’ll understand it mainly serves as a proxy, something that still communicates with Google servers. The fact is, there is no way around that. The whole Android ecosystem is dependent of Google, either because of Google Play services or Play Store"
(Emphasis added that Google is still required with microG)
Avoiding their location services is harder but micro-g does actually support other location services backends.
Push notifications is the problem child. When people "send" you push notifications, they actually send them direct to google and rely on google to send them to you. Installing micro-g can disconnect google at your end, but not at the app vendors end. It's likely that they will do this in many cases even if your phone actually lacks the software to receive the push from google.