They do, but group coordination is a lot harder than shipboard coordination. How many sailors you think actually remember how the fuck to do semaphore flags or Morse code?
And coordinating with flights in the air could be a nightmare if comms were disrupted. My guess is that SOP would be for those squadrons to abort and head for the nearest friendly landing strip.
What if the nearest friendly airstrip in range (accounting for fuel) is the ship itself? I'm sure they train for all kinds of situations, including a loss of communication.
Not saying it would never happen, but the Korean peninsula is a pretty crowded area geographically and modern planes have fairly large range. It wouldn't be a problem to fly to South Korea and land there, nor would it generally even be a problem to fly to Japan and land there either. Just try not to aim for China or Russia and you'd be fine (and even they MIGHT understand if NK was acting completely rogue and out of their interests.)
As for remembering morse code and flags, you'd probably be surprised. Especially if you have 4000+ crew on a carrier, you're likely to scrounge up a half dozen or so that do remember to put on the duty.
True jamming of radio communications would be difficult, however. Satellites are targets, of course. China can easily take one down. You could do a decent job over land you control with preparation of equipment to pump out massive amounts of RF energy. You could even do a decent job of annoying a particular target with a directed beam. But once again, short of detonating a nuclear weapon in the area, which would have other issues than simple jamming of the communications, you always have other frequencies and a nuclear powered ship can pump out a lot of RF energy in its immediate vicinity enough to get through any land based jamming and enough to keep a carrier group from bumping into each other. Aircraft might be an issue, but I'm sure they have plans for that, up to and including "Here is your mission, radios won't be an option, use your best judgement outside of mission parameters."