Not cheaply. It is an expensive process in terms of time and memory. Typically you would draw to a render target instead of the back buffer, drawing the render target to the back buffer, and using
Texture2D.GetData on the render target to get a section of the render target into an array. From this array you can read the colour of a pixel.
It is not an efficient process because modern GPUs are designed to have data going into them at very high speed, but not much coming back the other way.