Ellis is not a stalker.
Ellis is not a stalker. He's just a normal guy trying to pursue the girl of his dreams like he has been taught by society (movies, books, TV...).
We may not live in the same world but where I live, guys are supposed to take the first step and try to conquer the girl. And the girl, even if she indeed likes the guy, has to pretend she doesn't and play hard to get. And the guy has to keep trying despite the woman saying no because ''he knows'' she likes him. Eventually, she'll see how much he likes her, because he doesn't stop following her, and she will accept that she is in love with him... et cetera, et cetera.
She was smiling while rejecting him (an honest smile), she wasn't scared nor annoyed. In fact, she was surprised (in a good way) at how persistent he was being. And regarding the book donation, it was a joke for Christ's sake.
If, otherwise, she had believed he was a stalker, she wouldn't have been so nice. Normally, (again, in my world) if the female really doesn't like the guy, she won't reject him so politely,. She will be a lot nastier and much more hostile and firm than Adaline. She will make it clear that she doesn't like him, and, most definitely, she won't be smiling while doing so. And, if the guy keeps trying, she'll call a male friend or a group of female friends to help her get rid of the stalker.
Now, I'm not saying this is right nor wrong; and I personally don't like this method of courtship, (I don't think anyone should have to conquer anyone). But it's the way things are. The only movies I've watched where the woman takes the first steps are indie movies which are dialogue based and most people don't ever watch them, because, well, they're dialogue based . Then, there are the ones, also indies, where they're both active and passive, and alternate roles but this ones are even rarer. So, in almost (if not) all the mainstream films (which are the ones normal everyday folks watch), it is the guy that has to pursue and conquer the girl. And if he doesn't, even if she likes him, they won't get together because: Oh! God forbid women chase men!. Also, I constantly see this behaviour in the people around me, so it's not exclusively to cinema.
Anyways, as I've already said, like it or not, it's the way things are, and that makes Ellis a normal guy doing what normal guys had been told to do over many generations and not a stalker. (at least in my world, which is the real one, I don't know about yours).