Yes, it does silently and reliably upload all my photos to my server. That's like, the entire selling point of the app? You even have control over how and when (on wifi or not) and the ability to change hostnames depending on what network you are on. And yes I can browse my entire collection back to 2001 no problem. I have no idea what the offline support is.
That was my selling point for Nextcloud, and it turns out it doesn't work reliably. It works most of the time, but for backing up photos it's not enough, and when it fails it's super annoying (you have to resync EVERYTHING from scratch).
People seem very happy about Immich, I'm tempted to try. But people seem very about Nextcloud as well, so it's difficult to tell.