That is precisely how its done strider. A plane will not upright spin correctly if you input cross controls. The reason cross controls work in an inverted spin is because although the control inputs are opposite, the rudder is actually causing the plane to spin in the same direction as the ailerons did when they initiated the spin. You want to talk about not recovering, wait until you get an Ultimate Biplane into a true inverted flat spin.. You talk about non recovery. Its almost impossible to get it out of the spin without considerable forethought.
Your hypothesis is what will happen. Mainly because a trainer is going to want to self correct. Its almost impossible to get a trainer to maintain a stall condition. As soon as the nose drops its going to start flying again. As a matter of fact as soon as it develops any forward speed whatsoever it will start flying again.
Heres a video we shot of my 2nd flight on my new 35% Extra. At the 3 minute mark I did an inverted flat spin into an upright flat spin. This was just a test and trim flight and pretty conservative so there isnt much to it so dont expect a dazzling display. The angle is a little deceiving and it looks like the nose was pointing down just a little but it wasn't. It was flat.
http://kenvids.com/videos/Extra260-2ndFlight.wmv