I'm not aware of any method of directly using C programs in the control section of a PCI 7344 board, to replace the PID function. However, I can think of a few ways to achieve what you request with NI products...
The first big question that comes to my mind is...What is your Sampling Time requirement?, since this is really the gating element in trying to define a hardware/software platform to achieve your required algorithm needs.
You very accurately mention the two primary requirements for a servo or DC control, as an Encoder Input and an Analog Output Voltage.
Certainly the FlexMotion (PCI 7344) controller can be configured to read the encoder, and either using the onboard math and variable functionality, execute a preprogrammed algorithm to arrive at a desired output analog voltage, if the time needed to achieve this met your needs. Alternately, if it was fast enough, you could read the encoder up to the PC, process the algorithm on the PC and send a new analog voltage out to the FlexMotion.
There is however, another very interesting and potentially powerful way to achieve what you are trying to do, and that would be to use LabVIEW Real-Time capability with NI's Hardware and Embedded LabVIEW Real-Time software functionality.
In all cases, you could easily build most any algorithm as a set of LabVIEW VIs and as appropriate, load the appropriate functions to a FlexMotion embedded program, if it was the best choice for your Sampling Time needs and functionality, or if Real-Time LabVIEW H/W and S/W were the target, load the VIs there and use associated Analog Output and Digital (Encoder) input capability to interface to your motion system.
I believe that what you want is possible, it just depends on your target Sampling Time, your willingness to work with the products mentioned, and a bit of testing. Ultimately, if your project requires a sampling time that is not achievable either based on the program execution throughput of the products mentioned, or other constraint, then you may have to build a full custom solution...? But I think you could get it done with NI hardware and LabVIEW...
Hope this was helpful info for you...
