Should I apply?

You should speak to your guidance counselor about more appropriate schools. I’m going to go out on a limb here and say Harvard, Yale and Princeton have never accepted one student with a 1500/2400 SAT.

Look at it another way: Recruited athletes in the ivy league are thought by many to have lower GPA’s and test scores than non-athletes. Yale is not as forthcoming as Harvard, but when you look at Harvard’s athletic recruiting website, it’s spelled out very clearly: http://gocrimson.com/sports/mgolf/faq#Recruiting

If Harvard is looking for golf recruits with 2100+ SAT’s (700+ on each section) and 3.80 unweighted GPA’s, you can be assured the standards are NOT going to be lower for a non-athlete. Given that HYP are peer institutions, I would think Yale and Princeton’s standards are the same.