I know schools like Harvard aim high, but even people who have struggled prove to be just as capable or even better than the peers at Harvard. I was wondering if you, personally, know of anyone who has had "terriblish" grades in high school because they were unique and had a difficult past. Would writing about my past and gaining unique relationships with teachers at school mean anything to top-tier schools?
This is an extremely subjective question because I don't know what else you've accomplished in high school or why you ended up with low grades on your transcript. There are students out there who have been accepted to Ivy League schools with a few Cs, but they are very rare. Most of them will be legacies or athletic recruits (and even then it's an unusual situation). I assume there are also admitted students who come from rough backgrounds but show extremely high potential in specific academic or extracurricular areas, but it's uncommon. I don't think that unique relationships with teachers will help your chances because almost all other applicants will present similar credentials through their recommendations.
Also, keep in mind that the Ivies are very different from one another. They're all difficult to get into, but Cornell, for example, is significantly less selective than a school like Harvard.
I can't really give you more specific advice based on what you've written here, but I would say if you have stand-out achievements in certain areas that could make you the type of student that these schools want, go ahead and apply (provided it's not too much of a financial strain). Just make sure you have other safety options to fall back on in case it doesn't work out!