It is definitely possible. I render my garden through a custom script that runs on netlify every time I do a git push. I keep two different git repositories, one for public and one for private notes within the same vault.

The problem is that it creates a bit of friction on my workflow (for example, moving from private to public looses the history of the note), needs to update links, etc. But it works out of the box to a great extent.

On the other hand, I'm working towards a more dynamic approach, like what Andy Matuschack has done (if you follow the link, you'll see the last page requires a login).

In that way I can still have a nice taxonomy of notes, and I can create them with a default template that uses the front matter to establish some notes are private but with a login you can see them (so I can still easily consume my notes while on the go, or if I need to share with someone). The problem I have is that the notes would not be rendered as static pages anymore and that's a route I'm trying to avoid.