Just to take this one step further. Given that trim tabs can add to AOA, if the elevators froze in a neutral position and could not move for some mechanical breakdown reason, then dialing elevator trim tabs down (deflecting them up) would be a way to get your nose up, although it would only do so slowly due to the small size of the tabs.
Correct?
I'd think that it would only be possible for reversed-trim tabs to increase AoA if the mechanical design of the elevator caused it to be impossible for the elevator to be deflected to the point where it becomes less effective.
Pulling up elevator forces the tail down and increases the AoA of the wing. However, it's not necessarily a situation where "more is more effective". Beyond a certain "xx" degrees of deflection, the elevator is just going to increase drag without doing any more to lower the tail (or at least the ratio of "drag induced to performance increase" will worsen).
Imagine if you could move the elevator to 90 degrees straight up deflection (in relation to the stabilizer). It would cause a huge amount of drag, but wouldn't add any more AoA than "xx" degrees had. What is the "magic" point where more deflection equals more drag but equal or lesser-than maximum effectiveness?
To see what I mean drive your car with the window open and stick your hand out in the slipstream, palm down. Rotate your hand so that it "flies". Continue to increase the angle of rotation until you hit the point where your hand is palm-forward. At some point in there you'll no longer be "gaining lift" and will instead just be "gaining drag".
I would expect that a designer would give you enough deflection in the initial design to reach "best, most-effective" elevator deflection under "normal" control inputs... Plus some more deflection, "just in case". If that's the case, then going full-up deflection and then dialing-in "down" elevator trim would just take you further into the "more drag for less performance" realm.
Keep in mind that the drag induced at extreme elevator deflection is going to lower your speed as well, which makes it tougher (or impossible) to keep your nose up...