In order words, if I force quit an app, will it still be able to do background tasks when "Background App Refresh" is enabled?
Firstly: Don't force quit apps.
Secondly: No, still do not force quit apps. You might think it is a good idea doing this from time to time - it's not.
Yes, background app refresh may still be run after the app has been force quit. Note that it is "may" and not "will" as is always the case with background app refresh.