Would you have time to be in a sorority and major in pre-vet, or does one fall short?

Depends on the sorority. Some may be very focused on academia and therefore VERY good for you. Be sure to look at ALL of the options for sororities before you make a choice. Also check to see if there is a medical organization you can join on campus. Be open to sorority and non-sorority options.

As a member of Delts Sigma Theta Sorority Inc. it was my honor to pledge during my senior year having 26 credit hours.  One thing I learned is Sororities will be around until the end of time.  The important thing to remember is that its is better to consider a sorority when you are not focused on your major studies.  There are post grad options that are a tad more expensive but will allow you to focus on the founding principles, history, and service without distraction from your studies.  If you have great organizational management go for it!  If not then you'll need to prioritize your education first.