It would be quite straight-forward to measure the noise, rise and fall time, etc. on streamer outputs with the inputs shorted, but this is not particularly valuable since the streamer isn't doing any work under these conditions. I don't believe that there is any "reference" input signal that can be used to compare one streamer to another.
The amount of noise and jitter from a streamer will depend on how clean the input signal is and what the streamer is doing (e.g. what content is being played and how it is decoded).
So, while some kind of measurements are certainly possible, it's not clear how these would be useful in making comparisons. And correlating these measurements with the way a streamer sounds would be even more difficult.