Steven, granted carriers IRL do not make course changes while aircraft operations are in progress.
However you conveniently left out the key point of Rhinos' post. Carriers in real life operate with launch and recovery windows outside of which launching and recovery of aircraft unless it is an emergency situation is not possible. Something we do not do in Aces High. In order to allow for continuous carrier operations at will we have a happy compromise, it's called use your own common sense (OMG!).
Now taking off and landing from a turning carrier is nigh on impossible in an American aircraft. I almost never make it off but I've seen it done, Landing is generally not as hard but landing on a turning deck is easy to misjudge. I have done both in Japanese aircraft and seafires.
Unless I'm out of fuel and dead-sticking it in, I'll wait until the carrier stops turning. It's also easy to wait until the carrier stops turning to roll, just look left an right, the wake from the escort vessels will shoe you the way.
Landing is actually not as hard as it seems. You have to fly it in to the deck, line up on the far end of the carrier and maintain a level descent until you hit the deck and you will soon feel the reassuring thump of your wheels on the deck. As soon as you hit push your throttle full forward and hit your WEP in case you miss the wires so you can get back up and go around, if you get the wire you will stop.