Which of the following two questions are you asking:
1.) Is it possible to interface to the NI-5640R board via C function calls? In other words, can you configure the ADC, DAC, clock and other configuration via C?
In this case, the answer is No. NI-5640R can only be programmed via LabVIEW at this point.
2.) Is it possible to write your signal processing algorithms in C and then download them to FPGA on NI-5640R?
I have read that there are tools available in the market, that let you program your signal processing logic in a C-like language and then use compilers to synthesize gates. I am not an expert, but if this is the case, then we can try to get some answers for you.