I hope they will, but I’m a bit sceptical about how serious they are taking it since the beta version includes a proprietary maps app instead of say OSMand.
Also I doubt that their F-Droid fork will only include bonafied FLOSS like F-Droid does since they say it will include 60,000 apps.
It’s a little thing, but if they manage to do that and don’t include more proprietary stuff in their OS than Lineage I’ll switch over (and first thing I’ll do is install a different launcher). Currently I’m blocking all G%$&e domains and 8.8.8.8. via hosts file (Adaway). Because of that I have to block all “This Wifi has no internet connection” notifications and I even ban the Wifi and mobile network symbols from the status bar. Instead I’m using orbot’s onion symbol to indicate whether I have a working internet connection or not.