It's always been my understanding that CT keeps the aircraft trimmed for level flight at your current airspeed only in the absence of control input, and any stick or rudder input overrides any trim settings by the fact that trimming only adjusts the point at which the surfaces come to rest at "neutral", so to speak. It doesn't alter the range of motion available for flight control.
Practically speaking there shouldn't be much of an effect for combat per se, save that your aircraft will tend to level in the absence of stick input. So if you're just letting your sights drift onto a target, you may notice it, but beyond that, any effect should be limited to the time it takes for the control surfaces to deflect the additional distance during stick input opposite of the trim setting (that is, the elevators will have to move slightly further when you nose down, if you have your elevators trimmed up).
I have always pretty much left combat trim on, save for specific instances, such as when I'm lining up a shot in an aircraft where the nose can bounce around a bit (Ta-152 comes to mind), in which case I simply trim in the direction I need my sights to move.
Also landing in the Ar 234 where trim keeps pulling your nose up quite severely.
Effectively I treat trim as windage and elevation adjustments on rifle sights. Most of the time, your battle sights (or just leaving it alone and using hold over in the case of a scope, that is to say, just leaving CT on and moving the stick) works just fine. But every once in a while, you'll adjust your windage or elevation.
But as I'm given to understand, you will never be fighting your trim settings for maneuvering.