Does this directly translate to:
Won't you look at a thing such as I?
の at sentence end can be a (feminine) way to add emotional emphasis. Especially in this situation when there is also なんて before it expressing despise towards わたし.
As Genos said in comments, the whole thing means "you won't even look at/acknowledge me". Also I'm assuming we're talking about this song and you can see that it's not a question:
わたしのことなんて、見てくれないの (and you won’t spare me a single glance)
You weren't completely wrong thinking that の means a question. Here's how の can be used as a question:
(rising tone at end) そうなの？ Is that so?