Motherboards do often make noises - actually any hardware that has electricity be it AC or DC going through a circuit will create a harmonic. The problem comes in when under certain instances the harmonic resonates at a frequency that can be heard. Most of the time the harmonic is outside of the range of most users ears.
In your instance I suspect what is happening is that when you are about to play a game the current load to your graphic card significantly increases and then plateaus once you are in the game. A major part of the current used to drive your graphic card is supplied by the PC i-e slot itself and any additional power that a graphic card needs is provided by the separate connectors normally a single 6 pin but in some cases a combination of 6 and 8 pins. Now that is all background scene settings. When your card goes from 2D to 3D and begins to draw power from the board, that results in components near to the slot having to work harder, they go from a neutral state to a load state. Often that transition results in a buzzing sound as the work load increases, but goes once the component has reached optimal working temperature. The fact that you have a loss of frame rate is not a good thing in my view. It suggests to me, based on your narrative, that the components are taking some time (the frame rate lag) to get up to optimal performance spec and that should not happen in my view. If this problem is able to be replicated with another graphic card then I would suggest you going in to the retailer and reproducing the effect. RMA would be a option I would consider.
Quick test to do - Furmark. If the problem occurs when you run furmark then it is not ideal at all.
