No they don't have to come off, look at the picture above, this unit is right on top of the carbs.

Have a helper start the car, look down carbs to see which one is overflowing with fuel.

Remove that one needle and seat as Dayclona shows. Hold nut with wrench, loosen screw with a large screwdriver, then remove the screw and lift off the nut from the top and see how far down brass needle valve is screwed down so you can put it back in at least that far down or a little bit more so your float level is lower than it should be. Spray some luberication on the threads before removing the brass needle valve from the carb. Turn it with that nut, you may be able to turn it by Hand to remove it. Clean it out and reinstall.

Don't touch the other needle and seats yet.

Restart and look down the carbs again to make sure the oveflowing fuel has stopped happening. It is possible to happen in more than one carb, but one is enough to do this to your car.

Engine should run better now, raise RPM to 1500-1800 to help clean the plugs, depending if the plugs will clean up on their own without replacing or cleaning them.