You can do this. The issue with the Arduino isn't that the C code is no longer working, it's that it no longer exits. Compiling LabVIEW for an Arduino and flashing it will replace whatever is on the Arduino.
In the case of a RBP, since it's a full compter with an OS, you can run multiple programs and so could run both Python and LabVIEW and interface between the two. labviewmakerhub.com has a lot of info about such a scenario in terms of easily running LabVIEW on a RBP, with some caveats. For instance you have to use LV 2014 and it's non-commercial only.
Alternatively, in both cases, Arduino and RBP, you can run LabVIEW externally on some other system like a PC and communicate to the Arduino/RBP over serial, ethernet, Wifi, etc. MakeHub also has some VI libraries to deal with this. You can find them on VIPM. they let you do things such as read/write raw arduino pins over serial or higher level tasks such as control motors.
I saw my father do some work on a car once as a kid and I asked him "How did you know how to do that?" He responded "I didn't, I had to figure it out."
