This procedure requires relatively modest extensions of current technology. Anatomical reconstruction from serial sections has been done for many years. Currently, only a very tiny piece of tissue can be scanned in this way at the resolution needed for circuit reconstruction, and the process is both slow and labor-intensive. Researchers are currently working to automate the process, increase the speed, and increase the sample size. Eventually these developments should permit the scanning of an entire brain -- but there's still a long way to go to that point (unless, of course, someone starts pouring lots of money into development).
As a word of caution, it may not be enough to capture just the structure of the neurons and connections; functionally relevant information is undoubtedly contained in, for example, the ratios of chemicals in the synapses and the distribution of ion channels in the cell membrane. Staining techniques will probably permit all relevant variables to be read during the scan, but it's something to keep in mind.