It will probably be more trouble than it's worth.
Most airports I've been at require you to take the device out of the bad and put it on a tray that goes through the scanner / x-ray machine. Even if it's buried in your carry-on luggage.
And I don't think those trays are big enough for a 27" screen
Also, I recall going SOMEWHERE they wanted me to actually power on the device. It was maybe 3-5 years ago (I forget where) so I don't know if that place still has that requirement. But if places still ask for that... powering on a laptop (via battery) is much less of a hassle than finding a plug to power up the iMac.
So your only real alternative is to pack it in your checked luggage, and I don't know how safe that's going to be.