As usual (for questions around Brian), GPT-4 is not quite correct 
Yes, if you do not have a threshold, a neuron does not spike, so the spike-based interaction (on_pre in Synapses) does not work. But you can also directly have the input to a post-synaptic neuron depend on a pre-synaptic variable, i.e. have a continuous interaction that is calculated every time step. This can be used to model all kinds of continuous interactions, e.g. gap junctions (electrical synapses), or complex synapse models. It can also be used to simulate rate models, with the only limitation that you cannot model delayed interactions in this way. We do not have a good example for this, but this discussion explains the general approach: Coupled Van der Pol oscillators
Hope that clears things up!