Unfortunately, I do not think that this is possible with JavaFX. The only thing that I can see that has a native peer is the Stage. You can verify this yourself by using a ui analyzer tool, such as WinSpy, or "inspect.exe" or "visualuiaverifynative.exe" from the Windows SDK.
From Mixing Heavyweight and Lightweight Components by Oracle:
There are two kinds of graphics components in the Java programming language: heavyweight and lightweight. A heavyweight component is associated with its own native screen resource (commonly known as a peer). Components from the java.awt package, such as Button and Label, are heavyweight components.
[...]
A lightweight component has no native screen resource of its own, so it is "lighter." A lightweight component relies on the screen resource from an ancestor in the containment hierarchy, possibly the underlying Frame object. Components from the javax.swing package, such as JButton and JLabel, are lightweight components.
In this case, JavaFX is just like Swing; a lightweight toolkit where the various ui components are all written in Java and do not have a native peer.