Salir means many things, all of them related to the idea of leaving/exiting. For the meaning that you want though, the dating implication, it almost requires that it be and action with someone either implicit or explicit. The usage is not unlike "to go out" in English, to say that "she goes out" might mean that she is dating, but that isn't implied. To say that "she goes out with him" implies so strongly that they are dating that you would assume that unless told otherwise.
So ella ha salido is just "she has gone out", while ella ha salido con él is "she has gone out with him".
I'm wondering why "She has left" is considered a correct translation of "Ella ha salido", but "She has gone" is not, if there is no "going out on the town" connotation. She has gone shopping (or swimming, or home, etc.), she has gone out (partying), she has gone on (she is deceased) - all have a different connotation of what "gone" means.
I am not sure of your question, but from what you wrote I believe that you are asking if salir also covers meanings of "having gone" as in "gone to do". The answer is no, since salir is pretty much limited to describing the "leaving/going out" actions.
The "go and do" something verb is ir, as in voy a nadar (I am going to swim), which is in this tense would be he ido nadando (I have gone swimming), and I verified that Ella se ha ido (She has gone away) also covers her euphemistic dying.