JavaFX is uses a language called JavaFX Script, you can get started with JavaFX script with a basic Java understanding, but again I dont think understanding Java is that important there. You might want to understand how Java code is compiled and executed on the JVM. But if you want to make use of the vast Java ecosystem then you would find it important to learn Java syntax. Also being aware of OOP principles is an advantage. With JavaFX 2- Java would have API to create JavaFX components right within the Java application (quite easily)- that way you need not learn JavaFX Script.
You can learn Java and JavaFX in parallel- But you have to understand why you would want to learn JavaFX. I had learnt it a year ago and after an internship at Sun, I havent been able to work on it. What I found a bit difficult was the lack of a GUI builder for JavaFX. I dont know the current status of GUI Builder but I remember seeing a demo of the GUI builder in one of t he conferences and found it to be top notch. And without the GUI builder- lot of time was spent in setting the layout (And when I was working on JavaFX 1.2 there was not much of layouts and less components as well). But with JavaFX 1.3 and JavaFX 2 (to be released) is see that there is quite a lot happening in JavaFX.
I would agree with Mohamed Sanaulla in that it is not crucial because JavaFX (currently) is based on a scripting language. However, if you do start to pick up JavaFX, one thing should become very clear: JavaFX becomes a much more power experience when you can leverage the functionality of custom Java classes in your applications.
So while it is definitely not essential to know Java in an attempt to learn JavaFX, it would absolutely benefit you to have even a basic working knowledge. Your experience will have more and more of an impact as the level of your root Java knowledge grows.