The list of parts I used to carry includes engine case, merged exhaust system, camber compensator, super diff, rockers, pushrods, pistons and cylinders, steering wheel, cylinder heads, dropped spindles, distributors and so on.
I always had signs that my suitcases were opened for inspection but I never had any problem with it. I had a collection of "baggage checked by TSA" (or something like that) notices
They once asked me to explain what are the parts I had with me and the funny thing is that the lady couldn't understand a word, even if I was speaking English.
-"Merged 4 into 1 header, bolt up rocker shafts, magnetic trigger that replaces points in distributor"
-"Errrr, eeee, OK"
You have to be careful with packing, but I never had anything damaged, so it can be done.