No, that is incorrect.... Might I suggest you read AC 91-74A and the description of a tailplane stall caused by icing. It won't make it onto it's back, and didn't in any of the tests NASA conducted with full and deep stalls of the tail.
You have the AOA backwards, also. As the tail comes up the NEGATIVE AOA increases. To recover from a tailplane stall you MUST pull BACK on the yoke. Think of it this way.... the horizontal stabilizer is an upside down wing. Everything is opposite of what you would expect from a wing. As you pull back on the yoke the AOA increases since the high pressure area is on the bottom of the horizontal stabilizer. Therefor, moving the elevator up towards the sky increases the AOA by increasing the chord line. The plane will not flip over on it's back if the tail stalls.... It will, however, nose dive towards the ground... see the AC I cited
This is also covered in the Instrument Flying Handbook in Chapter 2 as I seem to recall.
Also,
all Cessna's have the elevator Flutter problem. It's one reason why flaps 40 was STC'ed inop on many of the early models and not available in the later models. That flutter was what we refer to as buffering on the main wings. The Wings would blanket out the airflow over the horizontal stabilizer and cause the airflow to become separated with the greater wing downwash from higher AOA and the associated lift being produced.