And I still haven't used Quick Resume (except once to test it) and always completely quit. Sadly I have a phobia about these things and think if I use it, my save files will be corrupted or it'll even damage the console! lol
Save files can't be corrupted by Quick Resume; when a game saves, it doesn't write the data itself or open any file handles. Instead it makes a simple data buffer in memory and hands it off to the Xbox operating system. The OS then handles the drive and cloud storage itself, entirely independent of the games actions.
Essentially the moment the game hands off this buffer, you could just immediately kill the entire game hypervisor (the OS container the game runs in) and the save data will still be 100% intact, because the game isn't controlling any of it. Quick Resume will be much the same, as it's just chucking the game's execution state to the drive and then closing the process.
As for the console, no this is impossible. Impossible like eating the sun, that is. Software cannot damage hardware*. NCIS and Bones are not even remotely accurate to how computers actually work. :P
Besides, all Quick Resume does is store the execution state to the drive. You can think of it like how save states work in emulators, except without the hardware emulation.
*Yes, you could have software configure things to overclock hardware to unsafe conditions, but that is extremely non-standard, and not something the Xbox has anyway. Also any program that is able to do that will require hardware capable of accepting the parameters, such hardware will also be designed not to accept unsafe parameters, so...