You woudl not extern "C" the class, you would need to extern "C" functions that will create your object and then call methods on it. CVI does not support classes since it is a C compiler, not C++. So have functions like Initialize that create an object of the class, and then wrapper functions to call member functions on the class. Then, extern "C" those functions and export them from the DLL. Then you will be able to call them from CVI.
Best Regards,
Chris Matthews
National Instruments