Unfortunately, there is no out of box PWA support at the moment. That said, it's possible to build basic support via customization. You can host the manifest file inside your statics folder. once thats deployed, it can be accessed via <hostname>/_msdyn365/_scnr/<staticContainer>/manifest.json. The staticContainer will change for each deployment. However the path is available to you as a global property to construct it dynamically (window.__publicPath__).
this way you can host and download the manifest file required for the PWA.
With regards to service workers, we support out of box serviceworkers that offer caching capabilities but there is no extensibility support at the moment that will let you customize service workers for your needs.