Yes, it is possible to get a rec when you or your family have no sorority affiliation, however, I would bet my last nickel you know several people who are Greek and just don't know it. Start asking your teachers and your friends Mother's. Yes, your local Panhellenic chapter can write a generic type rec, but it is much better for someone to write one that knows you. For example, if I was to write one for you it would say "I do not know this young women personally" type of thing. You can start the ball rolling by sending an email or telephoning the person in charge of recommendations. There is probably a website OR there might be a facebook page. Google your city panhellenic and see what comes up.
Arizona state recruitment is getting more competitive by the year. There is a recruitment story that was just posted on here about ASU
http://www.greekchat.com/gcforums/sh...d.php?t=122900. Remember that she was a junior and I think she says in the thread her grades were not great. You don't need recs, but if you were asking me about it I would tell you to get as many recommendations as possible. Many, not all, Chapters will invite you back after round 1 with a recommendation letter. The first round is only 20 minutes and unless you have a huge personality or light up the room when you walk through the door you sometimes get lost in the shuffle. With almost 1,000 girls going through you have to stand out to be remembered.
Way less stress then an SEC school, but you will still have stress. Recruitment is stressful I think at almost any big University. There are not a lot of bidless PNM's at ASU. They do a really good job at placing as many PNM's as they can. AS long as you don't single intentional preference you will probably get placed in one of the Chapters. I can not tell you how many go bidless at an SEC school because I have no frame of reference.
I hope this helps you.