The current is obviously traveling only a very short distance, and it's not very coherently directed, so the vector sum of all the currents is going to be small. It would be hard to measure, and much harder to harness.
But I'm curious. Does any of it radiate? I wonder if it at least makes a "pop" on a radio receiver nearby? My first guess would be that five billion amps, even very disorganized, would be audible on a radio at a reasonable distance, but...