Yes, this is possible using the 2.2 version of Visual COBOL, and the syntax is quite similar to the C# syntax.
As an example:
class-id a.
method-id main static.
invoke self::MyString("Hello")
invoke self::MyString
end method.
method-id MyString static public.
procedure division using by value passedString as string = " ".
display passedString
end method.
end class.