Okay, he definitely knows.
That huge description of the woman he's loved for a couple of years now all fits with her. They've been together for a few years now so the 'I realized it a few years ago' fits, the 'you probably know her' fits as it's HER, 'she's from a poor family' of course fits with Elijah, she's virtually hasn't a single penny to her name, the 'she doesn't know, we're not dating' description also fits completely.
No matter how you look at it, IT'S DEFINITELY HER.
Really, though, I have to applaud Elijah for her denseness, she's really oblivious to her surroundings.