In the 本 she does, but in the tv 表示する she might not for a while cos the 表示する is different than 本 . In this spoiler we can see that Elena is watching a movie from 1953 with stefan on it so maybe the "secret" will come out soon.
As the posts above have 発言しました that she does find out in the books, is correct. In the 表示する I'm not sure. But obviously at some point she will. But I'm guessing it's pretty soon. によって the looks of the new episode ' Your Undead to Me' it seems as if she is getting there. She might have found out. It would be so cool if she has. I wonder how she will react. I hope it isn't how Bella did. lol. Anyway but I hope I answered your question, even though people have done already. lol. x.
