If you don’t have the app does the website track your location on mobile or desktop?

If you have given the FB website permission to use your browser's location, then it could track you. If you haven't, the best it can do is IP location.

For example, if you try to login from an unknown computer, you'll get an email asking if it was you - that usually contains a rough location based on IP.

I am not sure because they could still potentially get it via their SDKs.