Absolutely! If you have not yet earned a first BA degree, you are eligible to participate in recruitment, and would be eligible to receive a sorority bid. Give it a shot and go in with an open mind.
Plenty of undergraduate students take graduate level classes as electives-- at least they did at my school. That won't affect your eligibility.
Good luck! If you go through formal recruitment and it doesn't work out, some of the sororities at your university may hold separate and more informal recruitment events later on in the school year to take in new members. Upperclassmen who perhaps did not get what they wanted out of formal recruitment may have a better opportunity in this process. That being said, formal recruitment is the best time to go through a recruitment, b/c you have the most options open to you and a chance to meet all of the sororities.
ETA: I meant to type in my previous post that you may want to consider a
non-collegiate SORORITY as an activity. Sorry about the confusion!