Yes the tunnel runs up to the base of where SAT 4 would be built. It only runs to SAT1 and SAT 2 currently. If it was to be opened in SAT3 they would need to totally remodel SAT3 as it has a totally different layout to SAT1 and 2.
In the current changes with STP (Stansted Transformation Project) SAT2 is going to have some sort of remodel. I heard rumors this could be to have it the same design as SAT1 with a link bridge for domestic arrivals and also just a refit so it will look like the way SAT1 has been changed to.