I'd have to vote yes on this one. Other experience in some other area of IT is an absolute must. But there's 2 basic types of DBA - those that work in development environments, providing information and guidance to development teams, and those who work in production environments, keeping systems up, available and responding well.
Development DBA's do best if they come from a programming background because they have the experience of understanding the requirements of application development and using database resources from the other side. Production DBA's that come from a systems administration / networks / OS background are more suited to the job of keeping systems up, understanding the need for reliable and tested backups, capacity planning and security.
I've never met a DBA that just did a short course and then got a job... probably because they wouldn't keep that job for long...