If I buy three monitors and game on one of them (the center), will turning off the two others while gaming ensure I do not lose any performance because of the two other displays being connected?
On the VGA port, there is 2 pins which you connect each other it will recognized as you connected to a monitor. If you connect VGA jack to monitor, the GPU will know that a monitor is added even it's turned off, only the information of the monitor won't transmitted to GPU, GPU will ignore it.
When you using a monitor and turn it off, the GPU will know that you still connect to that monitor but it's turned of and it'll not ignore that monitor, rendering on that monitor will still be there.
I've test this on HDMI also.
While rendering a typical game, unless the game supports multiple displays the other two outputs (and thus connected monitors) will not be part the game render. So the OpenGL/DX subsystem won't really be working extra hard to support the other displays.
Bottom line is you can rest assured and let the GPU do its thing, it won't affect your gaming performance.