The whole process of applying takes some considerable time and if you have read some of the threads you will also be aware of the long lead time into the courses , so if you are genuinely interested there is no reason not to start your application process sooner. In the past HR would allow people to defer their start date if they were at university and I cannot see any reason why they shouldn't still do that.
A university degree will not make you a better ATCO, it may however be a good thing to do on the basis that nothing in this life is certain and having the backup of a degree may give you a level of security.
To check that ATC is really what you want however, try to arrange a visit to your local unit and find out what the real day to day life is all about.
I am glad it wasn't my first career but on the other hand I wish I had realised about it sooner as I couldn't now imagine doing anything else.
Good luck in whatever you end up doing and if they still have University Air Squadrons I would suggest joining that.