Do you know the meaning of 'static website'? In some ways your question is an oxymoron. You're misunderstanding the term and have asked a bit of a silly question by accident.

By that definition, any static website that uses Google Analytics is no longer a static website, as it's interacting with a database.

As you point out, a static website (one that is deployed as plain HTML and some css / js / image assets) can be part of a larger ecosystem.

So maybe tone down the noob bashing...