I do a lot of recs every year and so do quite a few of my friends. We always advise getting recs, no matter where a PNM is going. Even if a Panhellenic site says they aren't required... if they address the topic and actually have a page/section devoted to info about recs including where to mail them...then assume they are important.
OP, Greek Chat has FSU listed as one of the schools where recs are mandatory, so I would not risk going through recruitment without them, even in the spring. Ask your Greek Life office when they will know which sororities are participating. I have a Panhellenic Facebook group of sorority alumnae and all we do are recommendations, so if you are having trouble finding recs for all the chapters you need, contact me through GC as the time gets closer.
