there shouldn't be a problem with security.
however, stowage when you're on the plane might be a pain in the ass. with regular back-packy stuff, you can stuff and squish it all until it fits under the seat in front of you. with the monitor, there will be no squishing. if it does happen to fit snuggly under the seat, you'll have to be real careful where your feet, and, if you're in the aisle seat, the feet of the people next to you, go.
i'm not sure of the specifics of how much room you have under the seat in front of you. as a rough estimation, i can fit my laptop, a bottle of water (back when you can still bring that type of contraband) and one foot side-by-side under the seat. i leave my other foot in the aisle (yes, i pull it in when people are passing by) or gently rest it on the backpack.
Let's not even get into putting it in the overhead compartments.