To answer your question let's look at how the typical OpenGL pipline works.
Vertex Shader -> Geometry Shader (Optional) -> Clipping -> Rasterization -> Pixel Shader ---------------> Fragments Merge.
I want to stress the fact that one pixel is not necessarily one fragment, multiple fragment can be combined to make one pixel, other fragments are discarded due to depth test , stencil test, blending. A Fragment shader will be executed for those fragments even though they might merged/discarded later.
I don't know a way give you exact number of the fragments in a scene, maybe there is a tool for NVidia or ATI than can give you how many times a fragment shader is executed.
Regardless of the actual numbers it's important to understand that due to the parallel nature of the GPU fragment shaders are executed on parallel on multiple fragments, it is also more important to profile your application and understand if it is GPU bound and if the bottleneck is in the vertex or fragment stage. here is a good article from GPU gems that explains how the GPU works.