It is possible to integrate Webdriver with FitNesse using Selenesse. I have made a start. Please find attached SlimSeleniumDriver.java file.
With this you can use the same commands in Selenesse / FitNesse, but change the underlying implementation to use Webdriver. I have changed some methods like the type and click to use Webdriver. Also added a method findElement() which used Webdriver to locate the element.
Almost all of the methods can be updated to use Webdriver.
I would love to make this into a complete working solution to use just webdriver API, but currently, it is in beta and has some issues. Hence for now using the WebdriverbackedSelenium approach works just fine (although it might affect the performance).
Thanks,
Ameya