Disregarding the feasibility of neurons within neurons in silico, the answer to
Is there any evidence for neurons existing within other neurons in humans or other organisms?
from a practical, biological point of view is no.
The literature point-of-view
The strongest argument against the neuron embedded (I'll deliberately not say "nested" as it has a computational and statistical taste to it) in another neuron is: I've never heard of it. I could cite every single neuro textbook I have not mentioning the phenomenon, but I'll wager that doesn't make too much sense, hence this unreferenced argument.
The physiological view
Neurons need a membrane potential to operate, e.g., to fire action potentials, or change their membrane in a graded manner. That membrane potential is, with perhaps an exception or two, always negative. That is, inside negative, outside neutral. A neuron within a neuron would provide inhospitable living conditions for the former. The latter wouldn't be too happy either. The former will not be able to build up the normal gradient of high Na+ outside the cell, and a high K+ inside, as the enveloping neuron would try to do exactly that same thing. The inner cell would thus build up a gradient (push Na+ out) and the enveloping cell would again transport the Na+ out. For K+ the reverse would happen (see Na+,K+-ATPase for background). In short, the inner cell would not be able to build up a membrane gradient, while the outer cell would have to deal with a pesky parasite messing up its ionic homeostasis. The inner cell would die, as many processes vital to the cell need a gradient (ion transport of nutrients along the membrane, disposal of garbage) and the outer cell would then finally be a happy neuron, barred the debris in its insides.
The teleological view
Physically embedded neurons don't make sense. Simply, because neurons exist, basically, to convey information from one neuron to the next. The textbook example of a neuron (Fig. 1) has an input part (the dendritic region), a space-traversing part to cover distance (the axon) and an output part (the axon terminal). Any processing occurring within the neuron is done primarily by logic operators such as summation, subtraction and integration (through the dendritic tree collecting information) and gain control (inhibitory or excitatory influences in dendritic region, cell body or axonal part). But in the end, a neuron is designed to get information from A to B. Therefore, a neuron within a neuron doesn't make sense from a neurophysiological vantage point.
Fig. 1. Textbook example of a motor neuron. The neuron receives information from higher motor areas in the dendritic region and stimulates the muscle using action potentials. Rate code is used to regulate the strength of muscle contraction. source: Obes DVR Lists.
- Purves et al. (eds.) Neuroscience, 2nd ed. Sunderland (MA): Sinauer Associates (2001). The Ionic Basis of Action Potentials