Understanding of the saturation function in the Monod-Wyman-Changeux Model
I don't have access to Sneyd's Mathematical Physiology, but in Wikipedia's description of the Monod-Wyman-Changeux model, they call Y the "fractional occupancy of the ligand binding site". Other references refer to it as the "fractional saturation".

In other words, it's simply the fraction of the binding sites which currently have ligands bound to them. The denominator, then, is the total number of binding sites, which is equivalent (for a unit volume) to the total concentration of the protein (i.e. the sum of every protein form) times the number of binding sites per protein. 

The numerator is the number of ligand-bound binding sites. Which is equivalent (for a unit volume) to the concentration of each form, multiplied by the number of ligands bound to it. So the zero-ligand forms are multiplied by zero, the one-ligand forms are multiplied by one, the two-ligand forms are multiplied by two, etc. (This doesn't reflect "doubly concentrated", rather it reflects the stoichiometry: for each protein molecule in the 2-bound state, there are two ligand molecules bound to it.)

So the answer to your boxed question is yes: that would be the appropriate form for a cooperative protein with three binding sites.