Is trimming for constant speed equal to trimming for constant angle of attack?
Short answer: Yes

Generally you are right. You are trimming the aircraft for a point on its polar, and that point is reached at a specific angle of attack.

You say yourself we should neglect secondary effects like the propeller blast, and under this condition you are right. Trimming means to set the distribution of lift between wing and tail surface, and this directly sets the angle of attack.

Now the more elaborate part of the answer

You trim the aircraft for a specific dynamic pressure, that is the product of air density and flight speed. If you slightly change your question from "trimming for constant speed" to "trimming for constant indicated speed", you gain precision and the answer is still yes. With a change in altitude you will also affect the Reynolds number the aircraft flies at, and the same polar point is reached at a slightly higher angle of attack the lower the Reynolds number gets when the aircraft climbs into colder air.

In turns the lift demand is increased. Not changing trim during a turn will let the aircraft speed up to increase lift at an unchanged angle of attack. That is why you pull more when turning - you want to increase the angle of attack, so speed can stay constant. When speeding up, you again change the Reynolds number and indirectly also the angle of attack, but this effect is very small.

When you change the power setting, you add energy to the aircraft at a different rate. Thrust becomes bigger and is counteracted by the sum of drag and the component of weight which acts in parallel to the thrust vector. Now the vertical component of weight is reduced, and so is your need for lift - but ever so slightly. This effect by itself means you will fly at a slightly smaller speed which will also very slightly affect the angle of attack. But since you did not change trim, the distribution of lift between wing and tail is unchanged, so the angle of attack is the same, save for a minuscule Reynolds number effect.

Increasing thrust will also increase the prop blast over the tail surfaces, making them more effective and slightly changing the balance of the aircraft. Depending on the direction of tail lift, the result is an increase or a decrease in angle of attack, but this is precisely the effect you wanted us to disregard.

Another secondary effect is a constant loss of weight as the engine burns fuel. This makes the aircraft lighter, so it requires less lift and a smaller angle of attack over time to remain at the same speed. Since you trimmed a specific polar point, the aircraft would need to slow down in order to stay at this polar point at its lower weight. But the lower weight also creates less drag, so instead of slowing down the aircraft will climb. Now the reduced density will require more angle of attack and will reduce engine output so in the end the same angle of attack is maintained at a higher altitude but a slightly lower indicated airspeed.