From what I know, HHN is a separate ticketed event. So, you could go to HHN only using your FF pass on nights that you would enter the studios after HHN opens. That would only be valid on days that FF pass is valid, it would have no impact on any other tickets you may have.
Now, if you were to do a Stay and Scream, that would mean you would be in the Studios before it closes (I think 5PM), so you would use you park ticket (using a day) by getting into the studios (or IoA or both) during their operating hours, for stay and scream, to stay in the park after hours, you would need to find a S&S locations, they would scan your HHN tickets (FF pass) when you entered the S&S area.