Mac App Store app updates, yes. macOS system updates, no.

AFAIK you only need an iCloud account to use iCloud related features, like the app store, syncing across devices, access to Apple services, etc. It's very much usable with just a local user.

Admittedly, they do heavily suggesting connecting an iCloud account.

You also literally can't even launch an iPhone past the initial screens without creating/logging into an Apple account. At least Google lets you use an Android phone without forcing an account.