Let's say a document is starting to register a service worker and is quickly going away before the service worker script is loaded.
Given the document is the fetch request client, it is expected that the service worker script fetch is terminated as the document is aborted. It then follows that the service worker never gets registered.

This can be tested in https://github.com/WebKit/WebKit/blob/main/LayoutTests/http/wpt/service-workers/register-then-reload.html.
Safari follows the spec (or my interpretation of the spec at least), while Chrome and Firefox seem to continue the fetching of the script and the registration of the service worker.

We should try to converge implementations and clarify the specification.