I get what your saying but its irrelevant. All who are free know the matrix isnt real just like the kid knows the matrix isnt real. They never explained how is avatar stayed instead of disappearing (or what ever happens to neo when he's free.)
IMO all he has to do is plug back and voilá the image he has of himself will appear.
If his RSI stayed then same is true for RSI of others who were freed from matrix? Why this isn't true for key characters being plugged into Matrix then?