Grips may affect how you shoot, and how you shoot may affect your choice in grips.
Ideally, the barrel will be in line with the long bones in your arm when you shoot. If the grips are too fat, you may have to turn your hand in order to reach the trigger properly. This is especially true when shooting double action, but not so much with a 1911, which is designed to fit small hands anyway. Turning the gun to reach the trigger affects both the direction and consistency of recoil.
You get the most consistent single-action results if you hold the gun with minimum side pressure, concentrating on your grip in the fore-aft direction. That way the recoil is straighter as the bullet travels down the tube, and subject to fewer variations with slight changes in grip. Shooting double action or simulated combat, you usually want a thicker grip for faster presentation, better control and reduced felt-recoil.
The difference between normal grips and thin grips on a 1911 is only about 1/8" in total. I doubt that has any effect on concealability. Shape of the butt (e.g., bob-tailed) and use of flush magazines is more important in that regard.