It's possible, it just works. I used to dual boot for years and I kept the Firefox profile on a shared drive. The only issue is that every time you switch OS it will not load extensions on the first run. You can fix that by launching the browser, closing it, then launching it again. I haven't had any other issues, and I would say that's just a minor inconvenience.
That been said, I haven't used Windows for a few months, so things might have changed.
Otherwise, if you don't mind using Mozilla Sync you can sync between different OS. Some extensions require you to explicitly enable cloud sync though, and some extensions do not support it at all. You will have to manually copy settings for such extensions.