As part of what I do I have to travel a lot,
I have an ibook and it is part of my body, I am taking it all over, anyway, No problems until now. the x-ray machines can not harm your G4.No way.I Passed it lid closed, lid opened, with or without the case. All okay
anyway of you look on the any airport website theu will tell you the same thing.
"The airport security X-ray machines will usually not affect hard drives nor the machine it self." bla, bla bla .....
as you are using a MAC probably you do not have "floppies " as they are affected the shilding not being as good as for the laptops.
Have a nice flight and enjoy Italy
P.S
(is where I am at the moment great food and lot of places to see )...