I have done in the past. By my own admission I cheated like mad though
I tied a 'special carp fly' in readiness for the experiment, a single #8 hook covered in deer-hair. Just like a Muddler minnow head, but
just the head, covering the entire hook shank.
Got the carp feeding happily on Chum mixers catapulted on to the surface, then cast the fly into the middle of them
They were so preoccupied sucking down little brown blobs that it only took a few seconds for the first take
In all I think I took about 20 fish that way on an 8 weight rod and line, using a 9 foot leader tapered to 8lb at the tip. I gave it up in the end as I could catch the carp more easily on real mixers with a 'proper' rod and reel, thereby avoiding the line burns that my left hand suffered from catching carp to just over 20lbs in a shallow estate lake on fly gear. Shallow water means that they can't dive when you hook 'em... they just take off at Warp 9 across the lake