Adding noise may make it a bit harder but does not fundamentally change anything. The measurements, especially over a network, are noisy to begin with and addin

Adding noise may make it a bit harder but does not fundamentally change anything. The measurements, especially over a network, are noisy to begin with and adding a delay will only add another noise source. Aside from that, time invariance is the wrong term, it is constant time. Time invariant means does not change over time, what you want here is data invariant timing, i.e. the runtime not depending on the data being processed.