I went through Recruitment twice at the U of I in the mid 80's. As an incoming Freshman I got recs to every house because that's what I was told to do when I went to an Alumnae Panhellenic meeting held in my hometown. I then withdrew after 3rd stage because I was so overwhelmed by the process. The next year I went through as a Sophomore and didn't bother with any recs, but by then I had a good GPA, was very active on campus and had a lot of friends in a bunch of Chapters. I don't know if that helps or not. It's just my story.
Obviously I don't know how things are today with Recruitment at the U of I. A lot can change in almost 20 years. But when I was on the other side as an active, recs were not that important for our Chapter simply because we didn't get that many. I have no idea how many PNMs participated back then, but it had to be well over 1,000. For some odd reason I distinctly remember all the recs we received easily fit into an average sized 3 ring binder. (By comparison here at the University of Alabama last year we had around 1,200 PNM's go through and our Chapter had at least 25 jumbo-size binders.)
So what's the bottom line? First, listen to anyone that has more current info than I do.

Second, recs can only help. They give the Chapter (hopefully) more information than what is required on your Panhellenic application. They also provide a personal opinion about you from an alum member which is very beneficial. My advice is if you can find alum members that are willing to write recs, then by all means do so. You never know when that little bit of an advantage may "put you over the top".