Does the cruise control still work if you go carb?
Yes. Maybe.
Would strongly suspect that the extra bracket for the bellcrank on CV carbs to accept the cruise control's actuator cable (they call it a stepper cable) has been obsoleted by Mother Harley. A company called Rivera Engineering used to make brackets for the E and G carbs and the Mikunis to add cruise to them. No idea if Rivera still making them though.
Even if gone from Harley adding cruise to an old Road King wouldn't scare me off. The bike's main harness will already have the cruise control wiring built in to. You'd need the cruise module and it's cable. Some kind of a little bracket to swing lower from the bellcrank could be fab'd up from scratch (I made one from spare bits several years ago -- if I can anyone can) if one were so inclined. Only other parts you'd need would be a pair of switches and a different set of switch housings on the handlebars.
You could re-use your original switches and just add the cruise switches. You can actually doing just adding the switch on the right side. That's the side with all the actual cruise control functions. The one on the left is just a master on/off switch. Instead of using that switch (pricey anymore) you could simply take the on/off wires to the toggle accessory switch that already exists on the back of the headlight nacelle.
If you stayed fuel injected the FI throttle bodies all have the connection point for the cruise cable. Would still have to add the module, cable, and switch or switches.