the trick is weight. it's not just size. i think carry on luggage is limited to 50lbs. now most mitx cases and components should be under weight, but any solid built micro atx tower & components will bump right up against that weight.
I am almost 100% certain that even a micro atx tower will be too big in one of the 3 dimensions to be carried onto a plane. Which means you're probably going to have to go with a small mitx rig... I know the Prodigy is WAY too big to fit in the overhead compartment, but something like the Silverstone SG05 or Coolermaster Elite 120, maybe even the Lian-Li PC-TU200B would likely be more along the lines of what you need.
general size restrictions for carry on luggage is something in the range of...
22"L x 14"H x 9"W... its the 9" requirement that's going to kill most non-ITX cases. Those three i listed above all fit those dimensions (barely); the prodigy doesn't come close, nor does the Corsair 350d (way too tall)