Yes. Nengo can use any sort of neuron model, including common non-spiking rate neuron models. Indeed, you can even change from spiking neurons to rate neurons in the middle of a simulation, or have a mixture of spiking and rate neurons in your model. Nengo also supports various learning rules.
You can also manually specify the connection weights between two ensembles of neurons. When you make a neuron-to-neuron connection, the transform of this connection is the weight matrix. See the inhibitory gating notebook for an example of a neuron-to-neuron connection.