Before I said anything, I wanted to arrange my facts.
Paraphrasing from the 2013 FSU recruitment guide, “The Tomahawk”:
Only fully matriculated FSU students who are enrolled as full time, are eligible to participate in fraternity or sorority recruitment, If chapters have active members who are not full time students in good standing at FSU, they are in violation of FSU policy. And this seems to contradict what Thetalady found on the FSU Greek Life page.
Here is the link (see page 8)
http://greeklife.fsu.edu/2013-Tomahawk
Undergraduate students are considered full time if they take 12-15 hours per semester. Any students taking under 12 hours per semester (spring or fall semesters) is considered part time.
http://registrar.fsu.edu/bulletin/un.../acad_regs.htm
(see "Course Loads")
Unless Panhellenic has made drastic changes to the Recruitment eligibility policies since Fall 2013 recruitment, a dual enrolled FSU/TCC student would not be eligible to join a fraternity or sorority at FSU until they qualified for full time status as a FSU student. I do know that some fraternities have bent the rule in the past, and it always came back to bite them. FSU does not lack for young women wanting to participate in Greek Life, so I cannot see them amending the enrollment policy to include dual enrolled students. In addition, for active membership,my sorority requires that a member be a full time student in good standing with the university where the chapter is located, so I am confused that the OP says her friend joined my chapter as a transient student.
So OP, as everyone has suggested, your best bet is to contact the Greek Life office at FSU to get the best answer to your question.