You're close to right here. But it's really the wing to tail relationship that trims to that AOA. But as long as it can hold that AOA you're dead right with this first part. Reduce the AOA of the wing and the plane needs to fly faster to compensate to hold altitude. If you don't add power the plane will descend increasingly if you hold the attitude until the uprising air meeting the wing is at the trimmed AOA.

You're describing what a lot of flyers THINK the plane should fly like and they'll go to great lengths to trick it into flying like this. Adding lots of downthrust is one answer so it combats the plane's natural tendency to lift the nose with additional airspeed. Generally you'll find that such people are those that have not flown in real planes or have only flown "simulators" and feel the need to "fix" their models so that they fly like they think they should fly rather than adapt to how they really fly.

Or if you're working with a hot aerobatic model then you'll be operating with the CG close to or even at the neutral point of the model. Such a setup requires extremely little or no "up" trim of the elevator compared to the wing. And when there's no "up" trim because the CG is so far back that the model doesn't want to fall into a dive on its own without some uptrim to hold the nose up then the model will not show a tendency to climb with increases in power or dive with decreases in power. But this last situation is an extreme case.

Normally we use SOME downthrust to limit but not totally eliminate the natural tendency to climb with added power. When set up this way the model is still fine to fly and flies in a way that most of the full sized planes fly.