I bet you can make the rudder system work.
You could make it "work", but you would need to:
1) Re-position the gudgeons on the transom and modify the deck lip (drill hole, cut away part of it).
2) Shorten the tiller arms.
Even then, there might be some interference with the mainsheet / traveler and the tiller crossbar. The rudders would also be higher, with less blade in the water.
As proof, here's an overlay of the two rudder systems on an 18's transom:
You'd need to add another gudgeon in the middle of the transom and hope the hole through the deck lip can support the upper part of the rudder system, because there's no space to put a gudgeon up there - and the backing plate probably doesn't extend that high anyway. The rudder would probably interfere with the drain plug if you didn't redrill it to rake it aft - which would mess up the helm.
Like I said, you *could* do it, but it would create a whole host of problems to be solved.