It's quite possible, up to a point. In fact, there is a new book "Functional Programming in Scala" that shows precisely how to do that. However, Scala is a fusion of OO and FP. Even its functional features are written in terms of objects. What you don't particularly need is mutable objects. But Scala's OO features -- notably traits -- are arguably useful for structuring code.

As the language designer himself has said: Scala is not a better Java, it is not Haskell on the JVM. I would add that it isn't just SML on the JVM either. It is much better, in my opinion, to embrace Scala for what it is, a powerful, expressive, pragmatic language for industrial use.