Okay, as checked baggage, you could. If you are going to, the previous advice of remove and separately box all heavy items with limited mount points like the gpu, and in addition seal the cooler in its own plastic bag because of the pressure changes... you never know. It might raise flags with TSA (or your local equivalent), but once they figure out what it is (which might involve opening it up) it should be allowed through.
My personal experience is I try to NEVER put electronics in the back of the airplane. I work for the airlines, and even I have ended up with several broken laptop screens, cracked hinges, and other miscellaneous damage over the past decade. Realize I travel a LOT, so many people will have no issues, but at this point any electronics I carry ALWAYS go in a small enough backpack that it stays with me up front in case you fly on a smaller regional aircraft and have to 'gate-check' what was supposed to be your carry-on.