Partly. It mostly works well for the things I use it (push messages, maps, exposure notifications seem to work too). Some apps behave a bit weirdly if the try to access specific API's, like Google Pay. So it definitely isn't fully functional, but works well enough for many use cases. There is also a LineageOS+microG fork, which makes trying it out a lot easier.

The way it works is that it pretends to be Google Play Services, so it isn't transparent to the apps. Not sure if the apps could figure it out it isn't running on the real deal.

For me it works great. You do need to use a special fork of LineageOS, because it needs to implement signature spoofing, which lineage devs refuse to do for security reasons. Get it from lineage.microg.org .

Once you have this fork it's great though, the spoofing is what makes it transparent to apps. It does use Google's push service as this is the only way (this is what the apps' backend servers talk to), but it doesn't require a google account, just a random ID.

The other things like geolocation don't require google services at all. In my experience it works great.