Incidentally most stall horns are designed to go off between 5 and 10 knots before stall, the POH will clarify for your aircraft. That being said a stall horn is not an indication of being in stalled flight but instead close to stalled flight.
As for if the aircraft is in fact in a stall or not during a falling leaf all depends on the aircraft and that aircrafts loading. I find most trainers will go in and out of stalled flight during the maneuver with typical loading. Now if you take and drop a 50lb ballast in the baggage compartment and put the CG closer to the aft limit I have found that keeps them closer to stalled flight throughout the maneuver. There is then less of that bobbing you are referring to and closer to a true falling leaf.
An actual falling leaf exhibits very little nose up and nose down bobbing of the aircraft but instead looks more like a leaf falling through the air. That is a slight sway of the nose from side to side, controlled by the rudder, while in full stalled flight. Typically requiring full rudder and causing banks up to 30-45 degrees with violent shaking of the buffet throughout.
Unfortunately trainers don't like to stay stalled which is why I recommend doing this with the trim wheeled back almost to the aft stop and with 1800-2000 RPMs. The ballast works best, but this will at least give you closer to the real thing.
The primary purpose of it is to demonstrate that rudder produces positive aircraft control when in stalled flight, ie right rudder equals right bank. I like to have my students at the end stop using the rudder and try to turn with the ailerons to show the negative aircraft control with ailerons in stalled flight, ie right aileron stalls left wing causing left bank. Caution though that this can flip you on your backside if your in a deep enough stall and the ailerons are jerked in quickly, an easy recovery just chop power, relieve back pressure, roll wings level, and recover from dive...but scares the crap out of you if your not expecting it.
Edit: Don't forget to idle the power on the recovery!!!!
That cover everything on the falling leaf for you?
