I'm sure you can put the scanner in a box and have it in a carry on bag. I've done that for a few years. I wouldn't trust putting under the plane I've seen someone throw bags on the ground like it was nothing...
i've had friends that have taken their scanners on the planes
the general public DOESNT know what a scanner does and what it is!
in this post 9/11 US, i wouldnt start waving it around all over if I were you
Get your ham license and carry a legal HT that also happens to scan. I've done it for years and only had one time recently when a screener saw a "spike looking thing" on the x-ray and went digging around for it. When he pulled out the radio, he said Oh, OK and put it back in. No problem.
I don't listen while in flight, as much as I'd love to!
I have taken my scanners and portable HT's on the plane and listened to the Air traffic before and after take off the only issue is if you have it on while on take off they will tell you to turn it off. I wouldn't go waving it around like said previous but, there should be no issues. If asked if it's a radio remind any air crew it does not transmit a signal that is what they might have a concern with.