Figuring out how an RF pulse affects the MRI spins
Yes, it basically is that simple. If the resonance frequency of the spin falls in the frequency range that the pulse excites, the spin will be manipulated by the RF pulse. Reality usually kicks in when you have imperfect slice profiles (i.e. to achieve a perfect rectangular slice profile, you would need an infinitely long RF sinc-pulse).

Is it possible that you accidentally mixed up angular frequency and normal frequency? I am asking, because your frequency spread and RF bandwidth would excite $\frac{2000\,\textrm{Hz}}{639.7\,\frac{\textrm{Hz}}{\textrm{slice}}} \approx 3.12\,\textrm{slices}$, if I am not mistaken, and... when it comes to frequencies and a ratio is so close to $\pi$, and there is a "/2.0" in the original question, there could be something going on with wrong frequency units.