You might want to check this out. If they sense you are using them as a fall back you probably WILL be rejected.
http://www.palmbeachpost.com/news/news/local-education/why-cant-i-get-into-uf/nSWJW/
Another point…what exactly do you expect to gain if hypothetically you do gain admission to AN Ivy? What exactly would a degree from say Columbia net you(other than debt) than one from UF or any other reputable University?