AI "neurons" (ie. combination of weight layer and following activation layer) are only a very crude model of the real thing, but they do model what appears to be the core function of integrating the synaptic inputs and firing in non-linear fashion when this integrated input crosses some threshold. So, it's more than just connectionism, but a lot less than attempting to closely mimic biology.

Nobody knows how much would be gained by using a more biologically accurate model of a neuron. Much of the low level detail may be irrelevant, but the timing aspect of it, or some equivalent, might be helpful if we want to make ANNs capable of learning realtime pattern recognition and control.