The question could be re-phrased to make it clearer or more precise, but the gist of it is clear enough. The OP is asking whether relative clock rate, which changes with distance from a gravitating mass, is sufficient to explain gravitational lensing.
It's not useful to say "No, a light ray follows a geodesic in curved space", because the change of relative clock rate with distance directly corresponds to space curvature. So the correct answer to my rephrasing of the OP's question is "Yes, the relative clock rate variation vs distance does cause the curvature of a light beam's path."
But the OP's question has another component that should be addressed as well. He is imagining that a photon has a spatial extent, and that if the clock rate on one side of the photon is a bit different than the clock rate on the other side, the photon will be deflected toward the side with slower clock rate. His intuition is basically correct. See this paper, "Comparison of the Phenomena of Light Refraction and Gravitational Bending". Clock rate variation due to gravitation can be modeled as a variation in a quantity analogous to refractive index.
The model is not quite correct (because refractive index does not affect a light wave's frequency, whereas gravitational redshift does), but by analogy, for photons one can think of space as having a higher refractive index where gravitational potential is lower (closer to a gravitating mass). If a photon is thought of as a wavefunction rather than as a particle, the wavefunction is indeed spread out in space; and it propagates very much like a classical light wave. Much like a light wave passing through a gradient index lens, the photon's wavefunction will be distorted as it passes through the region around a gravitating mass. This is an analogy, not quite a correct model -- but it can be useful.
