I go to KU and actually rushed as a sophomore transfer with NO recs whatsoever.
I never felt like rush was "competitive" exactly, but with so many girls and 13 chapters, it's definitely necessary to stand out. Recs and legacies are basically a way to get a chapter's attention so that they can find out how wonderful you are.
I ended up in a great sorority that I absolutely love, but I got cut from a LOT of houses (all but two!) because I didn't know how important recommendations were, and I didn't know many Greek alumnae.
And just a note, I'm being 100% genuine when I say that ALL of the sororities at KU are great! Some of them are more competitive than others, but even a so-called "lower tier" chapter has tons of smart, athletic, talented girls who are active all over campus.
So get some recs, practice playing up your best assets, and get ready to sweat. Recruitment in August on a hilly campus is no picnic.