by "Mozilla approved" do you mean that it has to come from the official add-on store?

because in my experience, it doesn't--I've installed a couple of extensions manually by just dragging the .xpi into the window.

Extensions in Firefox are required to be signed by Mozilla. If you make your own build of an open-source extension, it will not load. The setting to disable this check only works in Developer Edition, ESR and Nightly builds.

https://support.mozilla.org/en-US/kb/add-on-signing-in-firef...