I would not go past the little fence just south of the Port-A-Potty. It is not clearly labeled due to weather but the signs say NO TRESPASSING, NESTING MIGRATORY BIRDS, etc. etc.

The other side of the tracks should be an OK spot from the perspective of it being a National Park. Never saw a sign saying not allowed to go there. Your problem will be getting past the tracks (heavily fenced in, high voltage that kills on contacts, the tides if deciding on going under, etc.) and the before mentioned wildlife restriction.
Finally, the land moves away from 31L/13R and not closer once you get on the other side. It may not be as ok as you think.

Also check out Wikipedia here re: some old fishing grounds and actual subway stops to get off

http://en.wikipedia.org/wiki/Goose_C...IRR_station%29

http://en.wikipedia.org/wiki/The_Rau...IRR_station%29