i don't think it would be so simple and i don't think you can abstract neurons so hard, there are extrasynaptic receptors that react to concentrations of neurotransmitters outside synapses, and there are some neurotransmitters that leak out of synapses. thousands of leaking synapses can contribute to activation of some random receptor, or more than one this way. some other receptors are extrasynaptic by default and don't really have synapses, neuropeptides work like this but not only these. for gasotransmitters, effectively there's no concept of synapse. i don't think you can abstract all neurotransmitters to some one chemical messenger either, there are different ones with different half-lives, different diffusion rates, different metabolites some of which work in completely different ways. (steroids, neuropeptides, gasotransmitters, whatever lipids go into cannabinoid system, it's not just monoamines/glutamate/GABA/acetylcholine).

some receptors take multiple inputs, there are NMDA receptors that really only fire when glutamate and glycine both bind to it, and only after AMPA receptor nearby opens up first. we already know these things are important in forming of memories so it's probably a big deal. some of these receptors are ion channels, and some of these are important especially intracellular calcium