CT constantly trims your plane for level flight at full throttle regardless of what you are currently doing. Its only input is your current IAS.
In a dog fight the problem with CT is that it tends to make me bleed too much energy in a turn - If you hold the stick at a constant deflection, as your plane loses speed in the turn it keeps trimming you nose-up, i.e. increase your angle of attack for the stick deflection that you are holding. For this reason I tend to keep it off most of the time.
In a dive, CT will keep trimming you nose-down as speed builds up, making pull out ever more difficult. On planes like the 109, P-38, mosquito and some others it is almost a suicide device.
On the other hand, you generally do not want to be far off the "neutral" (i.e. level flight) trim. The compromise I adopted is to use the CT as a quick rough trimmer. When trim starts to bother me and I do not want to mess with the manual trims I turn it on for a second and immediately off again. I have it mapped to a button on my stick and go click-click when my speed changes and I feel "out of trim". In some planes the rudder needs a lot of trim input as speed varies (F6F for example, mosquito to a lesser degree). It is important to keep the slip/skid ball centered to conserved energy. Click-click, problem solved. I pulled some hard break turn and lost lots of speed, I find I keep constant back pressure on the stick - click-click, done. I am as close to trimmed as I need. For non-maneuvering flight, you have the auto-level, auto-angle and auto-speed (aka auto climb) trims.
One warning about turning CT on & off - do not do it while you are pulling Gs and in particular when the stall buzzer is buzzing. It will "jump" your trim instantaneously and you risk it pushing you beyond the stall and snapping the plane into a spin.
First please read this:
"Trim tabs are small surfaces connected to the trailing edge of a larger control surface on an aircraft, used to control the trim of the controls, i.e. to counter aerodynamic forces and stabilize the aircraft in a particular desired attitude without the need for the operator to constantly apply a control force. This is done by adjusting the angle of the tab relative to the larger surface.
Changing the setting of a trim tab adjusts the neutral or resting position of a control surface (such as an elevator or rudder). As the desired position of a control surface changes (corresponding mainly to different speeds), an adjustable trim tab will allow the operator to reduce the manual force required to maintain that position—to zero, if used correctly.
Thus the trim tab acts as a servo tab. Because the center of pressure of the trim tab is farther away from the axis of rotation of the control surface than the center of pressure of the control surface, the moment generated by the tab can match the moment generated by the control surface.
The position of the control surface on its axis will change until the torques from the control surface and the trim surface balance each other."
The sole purpose of Trim is to counteract aerodynamic forces on the aircraft in a particular desired attitude. One more time, The sole purpose of Trim is to counteract aerodynamic forces on the aircraft in a particular desired attitude.
it doesn't make the aircraft turn faster. The attitude of the aircraft is altered with a combination of control inputs, to move the rudder and ailerons on a given wing configuration the result of those inputs is a given attitude of the aircraft. If you alter the wing configuration (add or reduce flaps) the attitude will change and may or may not require a trim change as a result in the aerodynamic forces on the controls.
An aircraft that is "in Trim" performs better than an aircraft that is "out of Trim". Aircraft that are "out of Trim" will slow faster and require more energy to maintain altitude and cruise slower. If your stick controls will not allow you to pull enough G's to achieve a max performance turn and you are using trim to increase that AOA, then you need to re-calibrate your stick.