If you have more than 1 day at MK, I'd use a FP+ on HM, unless you're seeing characters.
I don't have kids and don't visit characters. I was there last week and HM consistently had the 4th longest wait time of the rides (behind Space, Big Thunder, and Peter Pan). It was up in the 30 minute range a lot of the time. That's not a huge wait time, but definitely FP+ worthy, IMO. Granted, Splash is closed right now, but HM would still be in the running if you have 2 days (and 6 FP+ entitlements to use).
Plus, the FP+ machine at HM makes a cool spooky sound. OK, maybe that's not a reason to use FP+ for this ride, but it's still cool...
If you have kids that want to see characters, HM probably isn't a good FP+ choice. The princess wait times get to be rather long!!
Oh, and to answer your original question, you do still go in the stretch room. The FP+ queue merges with the regular queue right before you get to the door to go into the stretch room.