When going through TSA security, there is always a chance they'll see something on the X-ray machine that looks a bit unusual, and they may want to open things up to take a look. I don't think it's very likely, but it's always possible. That's true whether it goes through carry-on or checked luggage, but in my experience, they tend to look more carefully at carry on baggage.
The lithium batteries of a drone should go in carry on, not in checked luggage. The rest of the drone can go in either.
Also, when you arrive at your destination, I believe you'll have to go through customs inspection. I have never travelled to Dubai, so I have no info on how intense their customs inspection might be, or whether a drone would cause any concern. In most countries, customs inspection is concerned with finding contraband or finding items where a duty or tax may be owed.