If the cross-section of the photon was spread out so that it hit both silvered and non-silvered parts, some would reflect, yes. But it wouldn't reflect quite like a mirror - diffraction effects would make things wonky, so people use half-silvered mirrors, which are nice.

How do they work, you ask? Did you ever take a course on wave mechanics where you calculated reflection and transmission coefficients? It's exactly like that, except now the probability is essentially what's "waving." (if you haven't, see here)