I doubt it.

The purpose of the longer derailleur arm is to take up the additional chain slack that's required by using wider gear ranges.

With Shimano, there are distinctly different road and mountain derailleurs. The mountain derailleurs use a different parallelogram to work with larger cassette cogs. I understand that the parallograms of road derailleurs, whether short or long cage, are the same. The parallogram is what follows the angle of the cassette, shifts the gears, and determines how crisp your shifts will be.

Campy is a little different. They specify different large cog capability for different cage lengths, but that changes for the same derailleur depending on whether you are using a double or triple crankset. That leads me to believe that the parallograms for Campy derailleurs, short medium and long, are also the same.

Through the years I've ridden with a variety of short and long cage road and mountain derailleurs. I can't say that I've found any shifting differences that I would attribute to derailleur cage length.