> Is it even possible to run Windows anymore without a Microsoft account?
Sure. On Pro you choose Organization/Domain setup and create the local account. Home is harder and the process keeps shifting. There are guides.
> If you only have a local account, OneDrive has nothing to sync to, right?
Mostly correct except if you have a local account and an MS login for Store/Office/etc. It isn't syncing automatically (so far) but could be triggered accidentally.
Another first today. I saw a dot next to my username (Start->username) that was naggy notification to MS Account myself.