Yes, it is certainly possible. You can start anytime. How you set it up would depend most on what you need for grade records. If your students are elementary age there is probably no real need for recreating past work in the planner (unless your school district requires it).
If your students are 9th grade or above, you will probably want to have enough data to create a transcript for graduation. You can just jump right in with spring semester work, but at the same time, you can enter grades from past semesters.
I would recommend watching some of the "How To" videos on our website and downloading a trial copy on your Mac to play around with OLLY and see if it will work for you.