Check it..
I've travelled 12 time zones and successfully checked:
20" iMac
24" LCD
30" LCD
Mac Pro tower (with the 'guts' in another suitcase because of weight).
You'll want a good suitcase, good luggage lock and good 'padding' for the iMac. You'll also probably want to remove the stand (it's not too hard).
I'm planning to do this with a 27" iMac in another 6 weeks.
Curiously, I just brought my Mac Pro back to sell (4 years later) and the case got a bit bent, mysteriously. The way it's bent is hard to understand - the suitcase is fine. After putting the RAM cards and HDDs back inside, everything's fine - just cosmetic outer damage, and that I hope to be able to bend back and correct. Never had an issue checking an LCD - but I'm a pretty careful packer. Heavy-weight sweatshirts provide good padding.