Can you D/R KT(debug/run Kernel task), and then modify the code, build, and then D/R KT again, WITHOUT rebooting the cRIO to stop the task?
Yes. Go to the Remote Systems window, right click on your program in the cRIO and delete it. There is code in the latest update that will kill all the tasks spawned by your program so it exists cleanly.
And by this, he means search for (typically) YourProject.out and delete that. 
You can see your program running in the debug window (the one above th break points) right click the top level and select terminate or terminate all. If you get a kernel crash from one of your programs you may want to reboot as reminates may get left behind, we wasted a long time on that.
Thanks for the clarification!
There is code in the library that is designed to cleanup properly when the main task is terminated. But the cRIO has no memory protection. So it is possible for a program with memory and pointer bugs to write all over anything else in the cRIO and cause it to be unstable. In those cases rebooting will guarantee that the new program run will work more correctly.