Surely the brain must be reasonably robust against very weak external signals - otherwise we could never think at all!
The thing I don't think you are realising is that if you sum signals from 10^6 neurons (say), those neurons will not be carrying identical information, but making their own individual contribution - so when you sum them you don't end up with anything that could be decoded.
As I said above, if you really take your concept of brain to brain electromagnetic communication seriously, are you putting in research grants to explore it, or thinking about experimental setups to demonstrate your theory?
I feel as though there is a special class of scientific 'theories' that are invented solely to debunk ψ research in general. These are theories that are never used in any other context, or even written up for peer review!