Is there a way to know how many sodium channels are active (conducting) at a given time in the brain?
Unfortunately, there is no way to know how many sodium channels are active (or even present) in one person's brain due to the extremely high variability of channel and neuron density in a population and the lack of methodology around quantifying total number of healthy active synapses (1). Diseases like epilepsy can occur due various points of the sodium signaling process going wrong. It could be sodium channels are deformed and not accepting the proper signal, it could a low density of channel proteins, or it could be damage to the neuron themselves (2-4). No one has examined the "normal/healthy range" of sodium channels in the brain. When categorizing sodium channel deficiency scientists will often compare the number of sodium channels in a healthy brain vs. a disease brain using bioluminescence imaging or some other visualization technique. Bioluminescence specially quantifies the number of active sodium channels by binding causing healthy sodium channels light up and then quantifies density by the brightness of the synapse. This is not a direct quantification of the number of proteins, but I can not think of any technique that allows you to count the number of proteins on a cell without damaging the cell. I'm sorry this isn't technically an answer to your question, but hopefully it provides some helpful references to understand molecular brain protein imaging. 


Principles of Neuroscience 
Low Sodium Channel Density and    Epilepsy 
Sodium Channel Mutations and Epilepsy/ Other Nervous    System Disorders
Neuropathy and Sodium Channel Related    Diseases