My school used to run rush this way. (Recruitment... whatever.

) Freshmen arrived on campus about 2 weeks before classes started. Rush began the day after freshmen arrived, and lasted 5 days for sororities, and about the same length of time for fraternities. The following week was "dead week" which was when academic orientation activities took place. Then classes started.
You didn't have to pre-register for sorority rush. There was an information session right at the start of rush, where you met the rho chi's and deaffiliated Panhel officers, filled out a registration form, and then were taken to your first round parties.
Dorms were open, but only to freshmen and upperclassmen with permission to return early.
Having rush before classes begin has the advantage that both PNMs and sisters/brothers can concentrate fully on rush without having to worry about class assignments and tests. Plus, PNMs haven't really been exposed to rumors/reputations/stereotypes, and may therefore be going in with more of an open mind. OTOH, deferred rush gives PNMs a chance to see what greek life is about, a chance to meet current members, and a chance to get acclimated to college life before going through the stress of rush. As with anything - it's a trade-off.