What effect would a stochastic metronome have on its listener?

Well, something like this is actually quite popular in modular synthesizers community. They have one type of modules called "Clock generators" which generate gate/trigger signals for given BPM (Like 1/4 or 1/8 or 1/16 rhythmic pulses for 120 BPM for example) and another type of modules called "Bernoulli gates", which basically allow to specify probability of input signal going to the output. Those beat-skipping metronomes with configured probabilities are then used to trigger notes or samples or whatever. Also, this is modular where you can modulate almost everything, including BPM itself, but that's a different story... Stochastic music approaches like this are often called "alleatoric music".