No it doesn't. Somebody following you by itself does not give you the right to physically attack them. Try going to court on a battery charge and explaining to the judge your reason for hitting somebody is because they were following you. You will lose.
What you're talking about is standard self defense. In Florida self defense is VERY different. All Trayvon would of had to have done was prove he had a reasonable fear of George Zimmerman.
Also to simply describe what Zimmerman was doing as "following him" is absurd. It was dark out, raining, Trayvon was on his way home, he noticed some person he didn't know staring at him from a car. Trayvon runs away only to see the person who was watching him from his car has no gotten out of the car and is now chasing him. We also know from the girls testimony that Trayvon had a fear that Zimmerman was possibly a rapist.
So taking all of that into consideration, yes Trayvon Martin would of had the right to stand his ground in Florida. Though I doubt it would have taken nearly two months just for police to arrest or charge him.