I've been doing some more concrete experiments with having Swing GUIs rendered by SFML, and as expected, I hit on a bunch of problems.
The awesome news is, the concept works and it will be possible!
But there is quite some work ahead.
Event dispatching will probably require me to implement my own simple focus manager, or get the existing Java one to work with JSFML somehow. The latter will be extremely tough, especially if you consider that you can add Swing GUIs to SFML windows inside another Swing GUI...
Another problem is painting. Apparently, after dispatching events (such as mouse enter events), control repainting does not have an effect immediately. I can't quite explain this behaviour yet, but I know that repainting the GUI every frame seems to be quite a performance killer and should not be the way to accomplish things.
I also failed to get the contents of JScrollPanes (and probably any other pane with embedded views) to render, but I'm fairly certain that there's some tricks to get them to work.