It is binary at one stage of processing. when a neuron has enough input it fires an action potential which is a binary one or zero. that then gets "read" by the synaptic terminal and turns back into an analog signal to a "post synaptic" neuron.
As you said, how this signal is then processed by the next neuron depends on a lot of factors including the effects of other neurons. Synaptic strength refers to the amount of electricity the post synaptic neuron sees given this binary 1 or 0 and is often measured at rest. However, if other neurons are firing it can go up or down, amplifying or shrinking it by activating other voltage sensitive ion channels or by increasing the conductance across the lipid bilayer of the cell so that the electricity leaks out of the dendrite of the neuron before it is processed at the soma (the cell body where a new action potential can be generated)

I'm a bit surprised the grad student or expert didn't discuss neuromodulators more. The fact is we already have the full connectome of a much simpler system, a worm (C Elegans). And this full mapping is considered insufficient to fully understand the simplified worm behavior because it doesn't fully capture the diversity of different neuromodulators and how they effect processing in neurons. It matters if the neuron is releasing dopamine, serotonin, glutamate, etc. There are ways to approximate these from EM images by analyzing the synapse properties, but ultimately it leads to a much larger problem in understanding neural processing.

In a similar light, the connectome project does not do a good job capturing synaptic strength. We don't really know just from the electron microscopy how strong the connections are. We can try and approximate it by looking at the size/formation of the synapse but ultimately this falls short.

For instance, my memory is that thalamocortical projections (thalamic nuclei to L4 of the cortex) do not make up the primary inputs to L4 on a structural connectivity level, but the strength of those connections are much stronger then the more numerous cortico cortical connections. I don't think the connectome from EM images will be able to pull that out.

The connectome is important, the same way knowing the human genome is important. However, it's really not going to tell us how to simulate a person. It's an important step to be sure, one we are still a good ways away from finishing last I checked (which was three years ago ...)