Since your question about runing LabVIEW code on the Arduino has already been answered (i.e. no) I'll tell you how I used Arduino for our robot.
With LIFA, Arduino is not really used like a traditional processor. It turns the Arduino into a very diverse, programmable data acquisition board.
We simply used a FitPC on our robot that was connected to an Arduino. So, it is entirely possible to do what you want with the Arduino if you get a FitPC or equivalent small PC that can run Windows and LabVIEW. The only downside to a PC+Arduino setup is that the time delay due to serial communication is not well suited for closed loop control implemented in LabVIEW but it can be done assuming you can deal with the large time steps.
