Since one of the classes I teach is AutoCAD I get asked about this a lot. Yes after 3 years if you still have a valid school email you can upgrade too the newest version, I like to upgrade every year just to keep up to date with changes in the program.
One thing that is not too well known is this applies to all Autodesk products, I currently have Inventor on both my computer at work, and my system at home. But you can get copies of all of their products including Fusion, Revit(used in architectural drafting) 3DS(used in video games and movies) and everything else on their catalog.
Just remember that you need an educational email address, they do check up on this periodically and you don't want your program locked out in the middle of a big project.