This is not correct. Aces high trim is exactly the same as moving your stick. But in real life this simply removes the pressure on the stick where you currently are holding it. If you are hands off in real life the stick moves when you adjust trim. This is accomplished by a tab on the back of the control surface which moves the opposite direction of which way you want the control surface to move.
This is how trim tabs work on almost all airplanes except a few that have a trimable horizontal stab or I have also seen simple spring adjustments on aileron trim on some planes.
Now the issue that we can not do like real life is that I can not remove pressure from your stick position with out you moving the stick. So if you would apply up trim you need to move stick forward to maintain the same pitch attitude. Now en order to still maintain full stick deflection the the scale of elevator to stick movement is adjusted as trim is so that you will stick have full stick deflection no matter where the trim is.
The only time trim can change your turn rates is when you are not elevator stop limited, but stick force limited because of high speed. In this case moving trim will add or decrease turn performance.
HiTech
I knew I explained it poorly... Autotrim moves my Elevators which are connected to the stick, so autotrim moving my stick moves my elevators, there is no separate trim tab.. so what I said was right but poorly explained.
But anyway, in observation, the P51 at low speed in a TnB manually trimmed 100% nose up will out-turn a P51 with autotrim on, because the stick isn't being moved forward and limited by the autotrim. And I am sure a P51 driver that gets into turnfights that require slow speeds and full flaps will observe the same, and have been doing so for many long years. It was something I picked up in 2008 thanks to PEZ.