Hey, CTO of Fission here! It depends on what you're trying to do. We actually bootstrap a js-ipfs node directly in the browser, so you always have an IPFS node if your app uses our SDK. It's even set up to communicate across tabs, including handling the security for that use case.
If you want to publish something that other people on the internet can see, then yes, you need a path off your machine, such as WebSockets. This can be a peer IPFS node, or to Fission's servers, or your own self-hosted node to provide availability.
Part of presenting to the offline-fist SIG was to get more support for parts of this, like communicating between a desktop node (e.g. go-ipfs) and your in-browser js-ipfs instance, which doesn't work out of the box today.
So IPFS handles the actual 'local first' aspect in the sense that once your data is cached, you can access it, and once you regain connectivity, it syncs again