I'd say that doesn't work, because the meaning is different. "I run after you" ("Eu alerg după tine") means that you are chasing me, i.e. you want to catch me.
"I run behind you" ("Eu alerg în urma ta") means that you are behind me and you are running. It doesn't necessarily mean that you are chasing me. Without any context, I'm likely to think that you aren't.