I'm a CS Major (still in school) I worked a 16month coop term working with databases alot. I wouldnt call myself a DBA because I did little managment as far as setting up user accounts managing roles and setting up backup schedules. I did mostly design & creation & poplulation (Used mostly SQL Server, although I have experience with Oracle and Postgres).
I would say understanding ERDs, SMDs, functional dependencies and all that wonderstuff is very important. School will show you the rules to proper database design and managment. It won't show you when you need to bend those rules and when you should not. You'll have to learn that from experience after you get out of school. However, for now learn and understand the rules.