Does a generator potential pass along a nerve the same way an action potential does?
Generator potentials (GP) are meant to generate action potentials (AP). An action potential results, whenever the level of depolarisation at a particular place crosses a threshold. This "place" is usually the beginning of an axon of a typical receptor, since it is equipped with all the channels required to begin and propagate an action potential. The purpose of the receptor architecture, then, is to make the threshold go off in a naturally meaningful situation.

There are two possible ways this is done. Say the neuron is transmitting information about the location of a stimulus. Then the "naturally meaningful threshold" would be some spatial cutoff, a minimum area that needs to be stimulated for the action potential to go off. Then, the receptor would have several GP-producing dendrites spread out, each generator potential being summed at the meeting place of the dendrites, which happens to be the cell body and the beginning place of the axon. So the individual generator potential in each dendrite will contribute to the sum, which will be summated and the cellular decision-making process (or a crude example of it) be affected as this summation. 

Another way is temporal summation, something which has, for example only one GP-producing dendrite and the axon. Then, for the summated potential at the cell body to cross the threshold, the stimulus must stay, or be summated across, for some time-cutoff. GPs have some decay time, before which if another GP reaches there, it adds up. This would be meaningful in things like the presence or absence of a touch, the cutoff preventing against minor fluctuations. 

This said, the situation in the eye in much much more complex. There are several layers of neurons and each neuron performs a lot of different functions and has a specialised architecture for it. The Rods and Cones actually produce hyperpolarizations and not depolarisations (theoretically, both are propagated in the same way, but hyperpolarisations themselves do not initiate AP). 

To complicate further, most receptor systems alter the frequency of AP and thus have some basal frequency, this modulation also being important for encoding the message. 

An image of GP: