is Progressive Web app fully supported by SharePoint?

What makes a PWA a PWA all resides in the browser layer. The web manifest and service worker are completely decoupled from the server-side. In fact they are more or less decoupled from the actual UI layer too. 

So yes, all server-side platforms like SharePoint support PWAs. You just need to reference a valid web manifest file with home screen icons, have a minimal service worker that you register with a simple script and of course serve the site using HTTPS.

I would think you can add the required references to include the manifest reference in your site's main HEAD element. And then drop a simple service worker registration script just before the close element.

What you program in your service worker is up to you.