This article should provide a helpful perspective: http://www.ni.com/newsletter/51675/en/
C was my first programming language. Then, I learnt assembly for 2 microprocessors, then C++, then LabVIEW, then TestStand.
Learning C helped me to understand memory management, which gave me insight into how LabVIEW does buffer allocations behind-the-scenes. TestStand has a very C-like structure, so knowing C made it easier for me to learn TestStand.
Learning assembly (together with digital logic) helped me to understand how software translates into hardware steps, which gave me insight into what the LabVIEW compiler needs to do behind-the-scenes, and it made it easier for me to learn the FPGA module in LabVIEW.
Learning C++ helped me to understand OOP concepts, which made it easier for me to learn LVOOP.
Note: This is my personal journey to my current state. Learning C (and the other languages I wrote about) definitely gave me a better "intuition" on how to write LabVIEW, but they're not strictly necessary. I don't think it's the most efficient pathway if your main goal is to improve LabVIEW skills. Other people have probably developed the same "intuitions" via other pathways.
Note also that I no longer use C or assembly these days. Although they were a good learning experience, I find them too unwieldy for my daily use cases. LabVIEW and C++ are now my preferred tools.
I'm guessing that's because the move from C to LabVIEW is a big paradigm shift, so they're simply struggling with a language that's "alien" to their "mother tongue". In fact, I experienced the same when going from C to C++! (They might have similar core syntaxes, but they're very different languages)
You might experience a similar struggle when you start learning C, but I highly doubt that it will degrade your LabVIEW skills. After all, LabVIEW is your "mother tongue" ;-)