I speak from experience when I say that they will most certainly give you crap about possessing a radio and probably likewise for a scanner. As far as legality goes, its not illegal to have a radio or scanner on at any time during a flight including takeoff, landing, taxiing and the works. For transmissions (if you're licensed to do so) that falls under the same rules as cell phones.....
Sorry, but this and every other post that says that it is not illegal and only an airline policy issue is completely incorrect. It is not the airline but the FAA that mandates ALL electronic devices be off during taxi, takeoff landing and flight below 10,000 feet. Further, anything that emits or receives any signal cannot be on at any point during the flight (again, that's the FAA, not the airline.). The exception being aircraft that have wifi installed and are TSO'd for wifi operation.
lastly you'll likely face the issue of to flight attendants razzing you about radios and scanners...my advise, if you don't want to waste your breath telling them that receiving a radio signal causes no interference to anything and isn't illegal then just keep it out of their view....
My advice, do not argue at all with a flight attendant ever. If it gets to the point that she/he/it comes up front to bring the problem to me, I dont care what the issue is or who says what, the mouthy passenger is getting thrown off my jet in a heartbeat.... you will lose that battle.
Here is the deal, it is not illegal to BRING any radios, scanners, ect on the plane with you. It is illegal to turn them on while on-board the aircraft. There are reasons the law is that way. Is a scanner gonna cause the plane to crash? no. do I care if someone, unknown to me, monitors coms during the flight? not in the least. Do I care if the Cart Donkeys are complaining in my ear about some tool in the back who is breaking the law and wont comply with their instructions, yes I do. Moral is: Dont get caught. If you do get caught, plead ignorance and politely do as your told.