if the size and weight is within the limit requried by the airline, it's ok. i just used one when i came here. what they care about is weight and size, not the type of the luggage.
sorry, what i mean is for the check-in luggage only. as for the handy luggage, i don't know. but i think, the package box of monitor is too big to be a handy luggage for most of the airlines. you may check with the airline you'll go with.