It depends entirely on your definition of "Competent Java Programmer".
A good understanding of the Java memory model and garbage collection strategies will help. As will experience with a wide range of 3rd part libraries.
On the other hand... if you're deeply indoctrinated into getter/setter dependency injection used by libraries like Spring, then you'll have to unlearn a lot of bad habits before you can properly deal with immutability - In this case, prior Java exposure is probably going to hinder you in learning Scala.
