Currently the LabVIEW FPGA Module can only target National Instruments' own FPGA products. Therefore there isn't a driver that will support other boards with FPGA's.
Quote from the license
...INSTALLATION AND USE OF THE LABVIEW FPGA TARGET MODULE FOR THE XILINX SPARTAN-3E STARTER BOARD (THE “TARGET MODULE”) IS LIMITED TO ACADEMIC INSTITUTIONS THAT HAVE A VALID, CURRENT “ACADEMIC TEACHING LICENSE” FROM NATIONAL INSTRUMENTS FOR THE LABVIEW FPGA MODULE. THIS TARGET MODULE MAY ONLY BE USED FOR INSTRUCTIONAL PURPOSES, SUBJECT TO THE TERMS AND CONDITIONS OF THE NATIONAL INSTRUMENTS SOFTWARE LICENSE AGREEMENT THAT ACCOMPANIES THE SOFTWARE...
And what about LabVIEW Embedded Module for ARM Microcontrollers ??
Is there same limitation ?
The LabVIEW Embedded Module for ARM Microcontrollers can be used to program over 260 ARM7, ARM9, and Cortex-M3 based devices only. Not sure if that's relevant to the original question you asked. To find out more about the list of ARM devices that are supported:
When using LabVIEW for ARM, the microcontrollers are typically programmed through JTAG. For specific ARM device support, you can take a look at the here: http://zone.ni.com/devzone/cda/tut/p/id/7066